High-temperature superconductor

Abstract

Formula (I): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q M p A y A’ s (I) wherein n, m, x, r, t, q, p, y, s, L, D, B, B’, Z, Z’, M, A, and A’ are as defined herein. These compounds can exhibit superconductivity at high temperatures.

Description

Cross - reference to related applications 【0001】 This application claims the benefit of U.S. Provisional Application No. 63 / 445,237, filed Feb. 13, 2023, and U.S. Provisional Application No. 63 / 353,487, filed Jun. 17, 2022, the entire disclosures of which are incorporated herein by reference. 【Technical Field】 【0002】 This disclosure relates to high - temperature superconductors, and related methods and devices. 【Background Art】 【0003】 In 1986, Bednorz and Muller announced a new class of superconducting materials with a critical temperature (Tc) significantly higher than what had been achieved previously, surprising the solid - state physics community [Bednorz, et al., Z. Phys. B 64, 189(1986)]. These materials are ceramics consisting of copper - oxide layers separated by buffer - layer cations. In Bednorz and Muller's original compound (LBCO), the buffer - layer cations are lanthanum and barium. Inspired by their work and motivated by his own measurements of the critical temperature under pressure, Paul Chu synthesized a similar material where the buffer - layer ions are yttrium and barium. This material, YBCO, is the first superconductor with a Tc exceeding the boiling point of liquid nitrogen (77K) [Wu, et al., Phys. Rev. Lett. 58, 908(1987)]. The highest critical temperature reported to date is 164K obtained by a mercury - based superconductor at a pressure of 31GPa [Putilin, et al., Nature 362, 226(1993), and Chu, et al., Nature 365, 323(1993)]. 【Summary of the Invention】 【0004】 This disclosure is based on the unexpected discovery that metal oxides containing alkali metal ions in their crystal structures are superconductors at extremely high temperatures (e.g., up to about 550 K). 【0005】 In one aspect, this disclosure relates to a compound of formula (I): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q M p A y A’ s (I) wherein n is a number from 0 to 3, m is a number from 0 to 6, x is a number from 0.1 to 1, r is a number from 1 to 8, t is a number from 0 to 1, q is a number from 0 to 6, p is a number from 1 to 7, s is a number from 0 to 20, y is a number from 0 to 20, L comprises at least one metal ion selected from the group consisting of transition metal ions and post-transition metal ions, D comprises at least one element selected from the group consisting of elements of Group IIIA and Group IVA of the periodic table, B comprises at least one first alkali metal ion, B’ comprises at least one first ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, Z comprises at least one second alkali metal ion, Z’ comprises at least one second ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, M comprises at least one transition metal ion, A comprises at least one anion, and A’ comprises at least one halogen anion. The compound of formula (I) is a crystalline compound. 【0006】 In other aspects, the present disclosure relates to a compound, wherein the compound is a crystalline metal oxide containing at least one transition metal ion (e.g., Cu ion), at least one alkaline earth metal ion (e.g., Sr or Ca) or at least one rare earth metal ion, and at least one chalcogen anion, wherein 10% to 100% of the at least one alkaline earth metal ion or at least one rare earth metal ion is replaced by an alkali metal ion, and 10% to 100% of the at least one chalcogen anion is replaced by a halogen anion. 【0007】 In other aspects, the present disclosure relates to a method comprising: (1) mixing a crystalline metal oxide with an alkali metal halide containing an alkali metal cation and a halogen anion to form a mixture, wherein the metal oxide contains at least one transition metal ion and at least one alkaline earth metal ion, and the atomic ratio between the alkali metal ion and the at least one alkaline earth metal ion is higher than 1:1; and (2) sintering the mixture at a high temperature to form a crystalline compound containing the alkali metal cation and the halogen anion. 【0008】 In other aspects, the present disclosure relates to a method comprising: (1) mixing a metal oxide (e.g., CuO and Bi2O3) with an alkali metal halide containing an alkali metal cation and a halogen anion to form a mixture, wherein the metal oxide contains at least one transition metal ion, and the atomic ratio between the alkali metal ion and the at least one alkaline earth metal ion is higher than 1:1; and (2) sintering the mixture at a high temperature to form a crystalline compound containing the alkali metal cation and the halogen anion. 【0009】 In other aspects, the present disclosure is an apparatus that includes the superconducting compounds described herein and is superconducting (e.g., exhibits superconducting properties such as being able to conduct a superconducting current) at a temperature of at least 200 K (e.g., at least 273 K). 【0010】 In yet other aspects, the present disclosure is a composition containing the superconducting compounds described herein. 【0011】 In a further aspect, the present disclosure is a fault current limiting device, comprising: a superconducting material having a superconducting state below a critical current and a normal conducting state above the critical current, the superconducting material including a crystalline compound containing at least one alkali metal ion, at least one first ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, and at least one halogen ion; an electrical conduction element including the superconducting material; a pair of electrical contacts disposed at opposite ends of the electrical conduction element and configured to connect the electrical conduction element to an electrical circuit; and a heat sink in thermal communication with the superconducting material of the electrical conduction element. 【0012】 Other features, objects, and advantages will be apparent from the specification, drawings, and claims. 【Brief Description of the Drawings】 【0013】 【Figure 1】 It is a schematic diagram showing an octahedral cluster in the crystal structure of the superconducting compound described herein. 【Figure 2】Figure 2A is a schematic diagram showing the relationship between the energy bands of the Wilson rule and the materials according to the present disclosure, its Fermi level, and its corresponding conductance. Figure 2B shows the Fermi situation of simple metals and superconductors. Left figure: simple isotropic 2D metal. The Fermi surface appears as a 1D circle. Right figure: Fermi situation of the isotropic 2D superconductor according to the present disclosure. The Fermi volume appears as a 2D ring. Figure 2C shows a realistic isotropic Fermi situation. Left figure: schematic diagram showing the measured Fermi situation of Bi2212 [Norman et. al., Phys. Rev. B, 52, 615(1995)]. Central figure: schematic diagram showing the possible Fermi situation of a higher-temperature superconductor predicted by the present inventor. Right figure: schematic diagram showing the possible Fermi situation of an even higher-temperature superconductor predicted by the present inventor. 【Figure 3】 Figures 3A - 3C show known electronic structure results measured by ARPES. 【Figure 4A】 Showing known cluster calculations. The energy difference 2δ is plotted as a function of the distance between the buffer ions and the plane. a) Influence of buffer ion radius on 2δ. b) Influence of buffer ion charge on 2δ. c) Influence of buffer ion flexibility on 2δ. 【Figure 4B】 A table showing the characteristics of known cuprate superconductors. The critical temperature can be explained by the model described herein. For clarity, the crystal structures of LBCO and YBCO are shown. 【Figure 5】 A schematic diagram showing another exemplary crystal structure of the superconducting compound described herein. 【Figure 6】 A schematic diagram of a power transmission network and an example of fault current limiting. 【Figure 7】 A schematic diagram and example of a fault current limiting (FCL) device including a superconducting material. 【Figure 8A】 A perspective view of an example of a resistive FCL element. 【Figure 8B】 A plan view of the resistive FCL element shown in Figure 8A. 【Figure 8C】 A cross-sectional view through section A of the resistive FCL element shown in Figure 8B. 【Figure 9】FIG. 9A is a current-voltage plot showing the threshold current transition between the superconducting state and the normal conducting state of the FCL. FIG. 9B is a current-voltage plot showing the thresholds of the FCL at four different temperatures. 【Figure 10】 Schematic diagram of an example of an inductive FCL device. 【Figure 11A】 Perspective view of an example of an inductive FCL element. 【Figure 11B】 Plan view of an example of the inductive FCL element shown in FIG. 11A. 【Figure 11C】 Cross-sectional view of cross-section A of the inductive FCL element shown in FIG. 11B. 【Figure 12】 Schematic diagram of an example of an FCL device equipped with a cooling subsystem. 【Figure 13】 Schematic diagram showing an example of a micro-pulling down crystal growth apparatus. 【Figure 14】 FIGS. 14A - 14B are photographs showing examples of crystalline fibers. 【Figure 15A】 Micrograph showing an example of a sintered compound. 【Figure 15B】 Micrograph showing an example of a compound obtained by a micro-pulling down crystal growth process. 【Figure 16】 Graph showing an example of the magnetic response of a superconducting compound as a function of temperature. 【Figure 17】 Graph showing an example of the magnetic response of a superconducting compound as a function of temperature. 【Figure 18】 Graph showing the magnetic moment of Compound 1 as a function of temperature. 【Figure 19】 Graph showing the resistance of Bi2212 as a function of current at 20°C and ambient pressure. 【Figure 20】 Graph showing the resistance of Compound 1 as a function of current at 20°C and ambient pressure. 【Figure 21】 Graph showing the magnetic moment hysteresis of the temperature ramp of Compound 1. 【Figure 22】 Graph showing the resistance of Compound 2 as a function of current at 20°C and ambient pressure. 【Figure 23A】A graph showing voltage as a function of current for a first sample of Compound 2 at 20 °C and ambient pressure. 【Figure 23B】 A graph showing voltage as a function of current for a second sample of Compound 2 at 20 °C and ambient pressure. 【Figure 23C】 A graph showing voltage as a function of current for a third sample of Compound 2 at 20 °C and ambient pressure. 【Figure 24】 Figure 24A is a graph showing resistance as a function of current for another sample of Compound 2 at 75 °C and ambient pressure. Figure 24B is the XRD spectrum of Compound 2. 【Figure 25】 A graph showing the magnetic moment hysteresis of the temperature ramp of Compound 4. 【Figure 26】 A graph showing the magnetic moment hysteresis of the temperature ramp of Compound 5. 【0014】 Like reference numerals in the drawings refer to like elements. 【DETAILED DESCRIPTION OF THE INVENTION】 【0015】 The present disclosure generally relates to high temperature superconductors (HTS), i.e., compounds that exhibit superconductivity at high temperatures (e.g., 273 K to 550 K), methods for preparing the same, and uses thereof. 【0016】 In some embodiments, the high temperature superconductors described herein have the formula (I): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q M p A y A’ s (I) A compound, where n is any number from 0 to 3 (e.g., 0, 1, 2, 3), m is any number from 0 to 6, x is any number from 0.1 to 1, r is any number from 1 to 8 (e.g., 1, 2, 3, 4, 5, 6, 7, or 8), t is any number from 0 to 1, q is any number from 0 to 6 (e.g., 0, 1, 2, 3, 4, 5, or 6), p is any number from 1 to 7 (e.g., 1, 2, 3, 4, 5, 6, or 7), s is any number from 0 to 20, y is any number from 0 to 20, L contains at least one metal ion selected from the group consisting of transition metal ions and post-transition metal ions, D contains at least one element selected from the group consisting of elements of Group IIIA (e.g., B, Al, Ga, In, or Tl) and Group IVA (e.g., C, Si, Ge, Sn, or Pb) in the periodic table, B contains at least one first alkali metal ion, B’ contains at least one first ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, Z contains at least one second alkali metal ion, Z’ contains at least one second ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, M contains at least one transition metal ion, A contains at least one chalcogen anion, and A’ contains at least one halogen anion. The compound of formula (I) is a crystalline compound. In some embodiments, the compound of formula (I) is a single-phase compound. In some embodiments, the compound of formula (I) is a single-crystal compound. 【0017】 Generally, n, m, x, r, t, q, p, s, and y may be integers or non-integers. 【0018】 In some embodiments, the first alkali metal ion is different from the second alkali metal ion. In some embodiments, the first alkali metal ion is the same as the second alkali metal ion. In some embodiments, the first ion assigned to B’ is different from the second ion assigned to Z’. In some embodiments, the first ion assigned to B’ is the same as the second ion assigned to Z’. 【0019】 In some embodiments, the element assigned to D is different from the metal ion assigned to L. In some embodiments, the element assigned to D is the same as the metal ion assigned to L. 【0020】 As used herein, "alkali metal ion" refers to an ion containing an element selected from Group IA of the periodic table, namely Li, Na, K, Rb, Cs, Fr, or a combination thereof. Generally, an alkali metal ion can have a valence of +1. In some embodiments, the alkali metal ion can form a molecular cluster having an effective charge of +1 to 0. In such embodiments, the molecular cluster can include one or more negative ions near the alkali metal ion, such that the positive charge on the alkali metal ion is compensated by the negative charge on the negative ion. 【0021】 As used herein, "alkaline earth metal ion" refers to a metal ion having a valence of +2 and containing an element selected from Group IIA of the periodic table, namely Be, Mg, Ca, Sr, Ba, Ra, or a combination thereof. 【0022】 As used herein, "transition metal ion" refers to a metal ion containing an element selected from Groups IIIB, IVB, VB, VIB, VIIB, VIIIB, IB, and IIB of the periodic table. In some embodiments, the transition metals described herein can be Sc, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Y, Zr, Nb, Tc, Ru, Mo, Rh, W, Au, Pt, Pd, Ag, Mn, Co, Cd, Hf, Ta, Re, Os, Ir, Hg, or combinations thereof. In some embodiments, the transition metal is Cu. In other embodiments, the transition metal is Fe or Zn. 【0023】 As used herein, "post-transition metal ion" refers to a metal ion containing an element selected from Groups IIIA, IVA, and VA of the periodic table. In some embodiments, the post-transition metals described herein can be Al, Ga, In, Tl, Sn, Pb, Bi, Hg, or combinations thereof. 【0024】 As used herein, "rare earth metal ion" refers to a metal ion containing an element selected from scandium (Sc), yttrium (Y), lanthanide series metals (atomic numbers 57 - 71), and actinide series metals (atomic numbers 89 - 103) in the periodic table. Examples of rare earth metals in the lanthanide series include La, Ce, Pr, Sm, Gd, Eu, Tb, Dy, Er, Tm, Nd, Yb, and any combination thereof. Examples of rare earth metals in the actinide series include Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, and any combination thereof. 【0025】 As used herein, "anion" can include simple anions, halides or halogen anions, chalcogenide anions, organic anions, oxoanions, pnictide anions, or any combination thereof. Examples of simple anions include those containing O, S, Se, Te, N, P, As, or Sb as a single atom. Examples of halides or halogen anions include those containing F, Cl, Br, I, At, or any combination thereof (IBr -3 , Cl2I -3 , Br2I -3 , and I2Cl -3 , etc.). As used herein, the terms "halide anion" and "halogen anion" are used interchangeably. Examples of chalcogenide anions include those containing O, S, Se, Te, and any combination thereof. Examples of organic anions include acetic acid (CH3COO - ), formic acid (HCOO - ), oxalic acid (C2O4 -2 ), cyanide (CN - ), and any combination thereof. Examples of oxoanions include AsO4 -3 , AsO3 -3 , CO3 -2 , HCO3 - , OH - , NO3 - , NO2 - , PO4 -3 , HPO4 -2 , SO4 -2 , HSO4 - , S2O3 -2 , SO3 -2 , ClO4 - , ClO3 - , ClO2 - , OCl - , IO3 - , BrO3 - , OBr - , CrO4 -2 , Cr2O7 -2, and any combination thereof. Examples of pnictide anions include those containing N, P, As, Sb, and any combination thereof. In some embodiments, the anions described herein can be anions containing any combination of F, Cl, Br, I, O, S, Se, Te, N, P, As, and Sb. In some embodiments, the anions described herein can be NCS - , CN - , or NCO - . 【0026】 In some embodiments, L in formula (I) can include Bi, Tl, Cu, or Hg. 【0027】 In some embodiments, D in formula (I) can include C, Si, Ge, Sn, Pb, or Al. 【0028】 In some embodiments, B in formula (I) can include Li, Na, K, Rb, or Cs. 【0029】 In some embodiments, B' in formula (I) can include La, Mg, Ca, Sr, or Ba. 【0030】 In some embodiments, Z in formula (I) can include Li, Na, K, Rb, or Cs. 【0031】 In some embodiments, Z' in formula (I) can include Ca or Y. 【0032】 In some embodiments, M in formula (I) can include Cu or Fe. 【0033】 In some embodiments, A in formula (I) can include O, S, Se, P, or As. 【0034】 In some embodiments, A' in formula (I) can include F, Cl, Br, or I. 【0035】 In some embodiments, the compound of formula (I) may satisfy the following equation: x*r + t*q = s. 【0036】 In some embodiments, the compounds described herein may include the crystal structures of a plurality of compounds of formula (I). In this case, the compound is called a superstructure or a twin crystal. 【0037】 In some embodiments, the superconducting compound of formula (I) is of formula (Ia): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q M p A y A’ s A” u (Ia) and may be a compound of. Here, n, m, x, r, t, p, q, y, s, L, D, B, B’, Z, Z’, M, A, and A’ are defined above, A” may include a halogen anion (e.g., F, Cl, Br, or I), and u may be a number from 0 to 20. In such embodiments, p may be any number from 1 to 3. Generally, A” may be the same as or different from A’. 【0038】 In some embodiments, the compound of formula (Ia) may satisfy the following equation: x*r = s. In such embodiments, the compound of formula (Ia) may also satisfy the following equation: t*q = u. 【0039】 In some embodiments, the superconducting compound of formula (Ia) is of formula (II): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q Cu p Oy A’ s A” u (II) It can be a compound of. Here, n, m, x, r, t, p, q, y, s, u, L, D, B, B’, Z, Z’, A’, and A” are defined above. In such an embodiment, p can be any number from 1 to 3. 【0040】 In some embodiments, the superconducting compound of formula (Ia) is of formula (III): L n D m (B x B’ 1-x ) r (Z t Z’ 1-t ) q Cu2O y A’ s A” u (III) It can be a compound of. Here, n, m, x, r, t, q, y, s, u, L, D, B, B’, Z, Z’, A’, and A” are defined above. In such an embodiment, q can be any number from 1 to 2, and r can be any number from 2 to 4. 【0041】 For formula (II), the superconducting compound subset is those where q is 0 or 1, and r is any number from 2 to 6. In such an embodiment, L can include Bi, Tl, Cu, Pb, or Hg; n can be from 0 to 4; D can be carbon; m can be any number from 0 to 4; B can include K, Rb, or Cs; B’ can include Sr, Ba, Ca, and Y; x can be a number from 0.1 to 1; and p can be 1, 2, or 3. 【0042】 Regarding formula (III), the superconducting compound subset is such that q is 1 and r is 2. In such an embodiment, L can include Bi, Tl, Cu, Pb, or Hg; n can be 0, 1, or 2; D can be carbon; m can be any number from 0 to 4; B can include K, Rb, or Cs; B' can include Sr; x can be a number from 0.1 to 1; t can be 0; and Z' can include Ca. 【0043】 Regarding formula (III), another superconducting compound subset is such that q is 1, r is 2, and t is a number greater than 0. In such an embodiment, L can include Bi, Tl, or Hg; n can be 0, 1, or 2; D can be carbon; m can be any number from 0 to 4; B can include K, Rb, or Cs; B' can include Sr; x can be a number from 0.1 to 1; and Z' can include Ca. 【0044】 Regarding formula (II), the superconducting compound subset is such that n is 2, m is a number from 0 to 4, r is a number from 2 to 8, q is a number from 0 to 3, p is 4, L is Bi, B is K, Rb, or Cs, B' is Sr, Z is K, Rb, or Cs, and Z' is Ca. 【0045】 Regarding formula (II), the superconducting compound subset is such that n is 0, m is a number from 0 to 4, x is 1, t is 1, r is 4, q is 2, p is 4 or 7, B is K, Rb, or Cs, and Z is Na. 【0046】 Regarding formula (II), another superconducting compound subset is such that n is 1, m is a number from 0 to 4, x is 1, t is 0 or 1, r is 2, 4, or 6, q is 0, 1, or 2, p is 1, 2, or 3, L is Hg, B is K, Rb, or Cs, Z is Na, and Z' is Ba. 【0047】 For formula (II), another subset of superconducting compounds is those where n is 1, 2, or 3, m is a number from 0 to 4, x is 1, t is 0 or 1, r is 2, 4, or 6, q is 0, 1, 2, 3, or 4, p is 1, 2, 3, 4, or 5, L is Tl, B is K, Rb, or Cs, Z is Na, and Z' is Ba. 【0048】 For formula (II), another subset of superconducting compounds is those where n is 2, m is a number from 0 to 4, x is 1, t is 1, r is 2, 4, or 6, q is 0 or 2, p is 1 or 3, L is Bi, B is K, and Z is Na. 【0049】 For formula (II), another subset of superconducting compounds is those where n is a number from 0 to 1, m is a number from 0 to 1, x is a number from 0.1 to 1, r is 2 or 4, t is a number from 0 to 1, q is 0, 1, or 2, p is 2, 3, or 6, L is Y, B is K, Rb, or Cs, B' is Sr or Ba, Z is Na, K, Rb, or Cs, and Z' is Y. 【0050】 For formula (II), another subset of superconducting compounds is those where n is 0 or 1, m is a number from 0 to 1, x is a number from 0 to 1, r is 2 or 4, t is a number from 0 to 1, q is 1, p is 2, 3, 4, 5, or 6, L is Cu, B is K, Rb, or Cs, B' is Ba, and Z is Na. 【0051】 In some embodiments, the superconducting compound of formula (I) can be a compound of formula (IV): BMAA' (IV) where B, M, A, and A' are defined above. Examples of such compounds include NaCuOF, NaCuOCl, KCuOF, KCuOCl, RbCuOF, RuCuOCl, CsCuOF, and CsCuOCl. 【0052】 In some embodiments, the superconducting compound of formula (I) can be a compound of formula (V): (B x B' 1-x ) r Z' q Mp A y A’ s (V) can be a compound of. Here, B, Z’, M, A, A’, x, r, q, p, y are as defined above. In some embodiments, a subset of the superconducting compounds of formula (V) is such that B is K or Rb, B’ is Ba, Z’ is Y, M is Cu, A is O, A’ is F, x is a number from 0.2 to 1, r is a number from 1 to 5, q is a number from 1 to 4, p is a number from 1 to 5, y is a number from 2 to 7, and s is a number from 0.3 to 4. Examples of such compounds include Y2Rb 4.5 CuO 3.5 F 3.5 、Y 1.5 Rb3CuO3F3, Y2Rb3Cu2F4O4, Y 2.5 RbCu 2.5 O4F 1.5 、Y4RbCu2O7F 0.3 、YRb2Cu 2.5 O4F、YBa 1.5 K 0.25 Cu2O 3.5 F 0.25 、YBa2KCu4O6F 0.5 、Y3Ba2KCu2O6F 0.5 、Y 1.5 BaKCu 1.5 O3F2, and Y2KCu5O4F 1.5 are there. 【0053】 In some embodiments, B’ is a metal ion having a first atomic number, Z’ is a metal ion having a second atomic number, and the second atomic number is smaller than the first atomic number. For example, B’ can be a metal ion containing Sr or Ba, and Z’ can be a metal ion containing Ca. 【0054】 In some embodiments, x in formula (I) ranges from 0.1 to 1 (for example, from 0.2 to 1, from 0.3 to 1, from 0.4 to 1, from 0.5 to 1, from 0.55 to 1, from 0.6 to 1, from 0.65 to 1, from 0.7 to 1, from 0.75 to 1, from 0.8 to 1, from 0.85 to 1, from 0.9 to 1, from 0.95 to 1, from 0.97 to 1, from 0.98 to 1, or from 0.99 to 1). In some embodiments, x in formula (I) is 1. Without being bound by theory, increasing the value of x increases the B' ions (i.e., alkaline earth metal ions or rare earth metal ions) in the crystal structure of the compound of formula (I) replaced by B ions (i.e., alkali metal ions), so it is considered that the critical temperature (Tc) of the superconducting compound of formula (I) can be increased. 【0055】 In some embodiments, t in formula (I) ranges from 0.1 to 1 (for example, from 0.2 to 1, from 0.3 to 1, from 0.4 to 1, from 0.5 to 1, from 0.6 to 1, from 0.7 to 1, from 0.8 to 1, from 0.9 to 1, from 0.95 to 1, from 0.98 to 1, or from 0.99 to 1). In some embodiments, t in formula (I) is 1. Without being bound by theory, increasing the value of t (for example, when t is greater than 0.5) increases the Z' ions (i.e., alkaline earth metal ions or rare earth metal ions) in the crystal structure of the compound of formula (I) replaced by Z ions (i.e., alkali metal ions), so it is considered that the Tc of the superconducting compound of formula (I) can be increased. 【0056】 In some embodiments, n in formula (I) can be any number from 0 to 3 (for example, an integer or a non-integer). For example, n can be any number from 0.1 to 2.9 (for example, from 0.2 to 2.8, from 0.3 to 2.7, from 0.4 to 2.6, from 0.5 to 2.5, from 0.6 to 2.4, from 0.7 to 2.3, from 0.8 to 2.2, from 0.9 to 2.1, from 1 to 2, from 1.1 to 1.9, from 1.2 to 1.8, from 1.3 to 1.7, from 1.4 to 1.6, or 1.5). 【0057】 In some embodiments, m in formula (I) can be any number from 0 to 6 (e.g., an integer or a non-integer). For example, m can be any number from 0.1 to 5.9 (e.g., 0.2 to 5.8, 0.3 to 5.7, 0.4 to 5.6, 0.5 to 5.5, 0.6 to 5.4, 0.7 to 5.3, 0.8 to 5.2, 0.9 to 5.1, 1 to 5, 1.1 to 4.9, 1.2 to 4.8, 1.3 to 4.7, 1.4 to 4.6, 1.5 to 4.5, 1.6 to 4.4, 1.7 to 4.3, 1.8 to 4.2, 1.9 to 4.1, 2 to 4, 2.1 to 3.9, 2.2 to 3.8, 2.3 to 3.7, 2.4 to 3.6, 2.5 to 3.5, 2.6 to 3.4, 2.7 to 3.3, 2.8 to 3.2, 2.9 to 3.1, or 3). In some embodiments, the sum of n and m is an integer. 【0058】 In some embodiments, r in formula (I) can be any number from 1 to 8 (e.g., an integer or a non-integer). For example, r can be any number from 1.1 to 7.9 (e.g., 1.2 to 7.8, 1.3 to 7.7, 1.4 to 7.6, 1.5 to 7.5, 1.6 to 7.4, 1.7 to 7.3, 1.8 to 7.2, 1.9 to 7.1, 2 to 7, 2.1 to 6.9, 2.2 to 6.8, 2.3 to 6.7, 2.4 to 6.6, 2.5 to 6.5, 2.6 to 6.4, 2.7 to 6.3, 2.8 to 6.2, 2.9 to 6.1, 3 to 6, 3.1 to 5.9, 3.2 to 5.8, 3.3 to 5.7, 3.4 to 5.6, 3.5 to 5.5, 3.6 to 5.4, 3.7 to 5.3, 3.8 to 5.2, 3.9 to 5.1, 4 to 5, 4.1 to 4.9, 4.2 to 4.8, 4.3 to 4.7, 4.4 to 4.6, or 4.5). 【0059】 In some embodiments, q in formula (I) can be any number from 0 to 6 (e.g., an integer or a non-integer). For example, q can be any number from 0.1 to 5.9 (e.g., 0.2 to 5.8, 0.4 to 5.6, 0.6 to 5.4, 0.8 to 5.2, 1 to 5, 1.2 to 4.8, 1.4 to 4.6, 1.6 to 4.4, 1.8 to 4.2, 2 to 4, 2.2 to 3.8, 2.4 to 3.6, 2.6 to 3.4, or 2.8 to 3.2). 【0060】 In some embodiments, p in formula (I) can be any number from 0 to 7 (e.g., an integer or a non-integer). For example, p can be any number from 0.1 to 6.9 (e.g., 0.2 to 6.8, 0.4 to 6.6, 0.6 to 6.4, 0.8 to 6.2, 1 to 6, 1.2 to 5.8, 1.4 to 5.6, 1.6 to 5.4, 1.8 to 5.2, 2 to 5, 2.2 to 4.8, 2.4 to 4.6, 2.6 to 4.4, 2.8 to 4.2, 3 to 4, 3.2 to 3.8, 3.4 to 3.6, or 3.5). 【0061】 In some embodiments, s in formula (I) can be any number from 0 to 20 (e.g., an integer or a non-integer). For example, s can be any number from 1 to 19 (e.g., 1.5 to 18.5, 2 to 18, 2.5 to 17.5, 3 to 17, 3.5 to 16.5, 4 to 16, 4.5 to 15.5, 5 to 15, 5.5 to 14.5, 6 to 14, 6.5 to 13.5, 7 to 13, 7.5 to 12.5, 8 to 12, 8.5 to 11.5, 9 to 11, 9.5 to 10.5, or 10). 【0062】 In some embodiments, y in formula (I) can be any number from 0 to 20 (e.g., an integer or a non-integer). For example, y can be any number from 1 to 19 (e.g., 1.5 to 18.5, 2 to 18, 2.5 to 17.5, 3 to 17, 3.5 to 16.5, 4 to 16, 4.5 to 15.5, 5 to 15, 5.5 to 14.5, 6 to 14, 6.5 to 13.5, 7 to 13, 7.5 to 12.5, 8 to 12, 8.5 to 11.5, 9 to 11, 9.5 to 10.5, or 10). 【0063】 In some embodiments, the compound of formula (I) can satisfy the following equation: x*r + t*q = s. In such embodiments, the number of alkali metal ions (or the valence electrons of alkali metal ions) is the same as the number of halogen anions (or the valence electrons of halogen ions). Without being bound by theory, it is believed that such compounds of formula (Ia) can form a more thermodynamically stable structure by forming an alkali metal halide salt layer. 【0064】 In some embodiments, the compound of formula (Ia) may satisfy the following equation: x*r = s. In such embodiments, the compound of formula (Ia) may also satisfy the following equation: t*q = u. In such embodiments, the number of alkali metal ions (or the valence electrons of alkali metal ions) is the same as the number of halogen anions (or the valence electrons of halogen ions). Without being bound by theory, it is believed that such compounds of formula (Ia) can form a more thermodynamically stable structure by forming an alkali metal halide salt layer. 【0065】 In some embodiments, the superconducting compounds described herein are crystalline metal oxides containing at least one transition metal ion (e.g., Cu ion), at least one alkaline earth metal ion (e.g., Sr ion or Ba ion) or at least one rare earth metal ion, and at least one chalcogen anion (e.g., O anion), wherein 10% to 100% of at least one alkaline earth metal ion or at least one rare earth metal ion (in the crystal structure) is replaced by an alkali metal ion (e.g., Li, Na, K, Rb, or Cs ion), and 10% to 100% of at least one chalcogen anion is replaced by a halogen anion (e.g., F or Cl). Examples of the crystalline metal oxide before modification (transformation) include Bi2Sr2CaCu2O y (Bi2212), Bi2Sr2Ca2Cu3O y(Bi2223), and YBa2Cu3O7 (YBCO). In some embodiments, the superconducting compound is the above crystalline metal oxide, and 20% to 100% (e.g., 30% to 100%, 40% to 100%, 50% to 100%, 60% to 100%, 70% to 100%, 80% to 100%, 90% to 100%, 95% to 100%, 99% to 100%, or 100%) of at least one alkaline earth metal ion or at least one rare earth metal ion in the crystal structure is replaced by an alkali metal ion. Without being bound by theory, superconducting metal oxides in which a larger amount (e.g., more than 50%) of alkaline earth metal ions in the crystal structure are replaced by alkali metal ions are thought to exhibit a higher Tc based on the following model. In some embodiments, the superconducting compound is the above crystalline metal oxide, and 10% to 90% (e.g., 15% to 85%, 20% to 80%, 25% to 75%, 30% to 70%, 35% to 65%, 40% to 60%, 45% to 55%, or 50%) of at least one chalcogen anion in the crystal structure is replaced by a halogen anion. Without being bound by theory, replacing a certain amount of chalcogen anions with halogen anions is thought to be able to form a thermodynamically more stable structure by forming an alkali metal halide layer. 【0066】 In some embodiments, the above crystalline metal oxide may further contain post-transition metal ions (e.g., Bi or Tl ions) or transition metal ions (e.g., Hg ions) as described above. In some embodiments, the above crystalline metal oxide may contain rare earth metal ions (e.g., Y) as described above. 【0067】 In some embodiments, the crystalline metal oxide may contain two or more (e.g., 3 or 4) alkaline earth metal ions (e.g., Sr, Ba, and / or Ca ions). In such embodiments, only one of the alkaline earth metal ions may be replaced by an alkali metal ion, or two or more of the alkaline earth metal ions may be replaced by an alkali metal ion. 【0068】 In some embodiments, when two or more alkaline earth metal ions in the crystalline metal oxide are replaced by two or more alkali metal ions, each alkaline earth metal ion may be replaced by any one of the two or more alkali metal ions. 【0069】 In some embodiments, the crystalline metal oxide may contain two or more (e.g., 3 or 4) halogen anions (e.g., F, Cl, Br, and / or I anions). For example, in the compound of formula (Ia), A’ and A” may be two different halogen anions. 【0070】 In some embodiments, the superconducting compounds described herein (e.g., compounds of formula (I)) are compounds having a crystal structure, the crystal structure comprising a plurality of unit cells, at least 10% of the unit cells comprising clusters (e.g., sub-unit cells), the clusters comprising a plurality of anions (e.g., O anions and / or halogen anions), a plurality of transition metal ions (e.g., Cu ions), and at least one alkali metal ion (e.g., Li, Na, K, Rb, and Cs ions), each transition metal ion forming a covalent bond with at least one anion, the plurality of anions defining a plane, at least one alkali metal ion being positioned proximate to the plane, the distance between the at least one alkali metal ion and the plane being less than twice the radius of the at least one alkali metal ion, and at least two of the plurality of anions having a distance of from 3.8 Å to 4.2 Å. In some embodiments, at least two of the plurality of anions can have a distance of at least 3.8 Å (e.g., at least 3.85 Å, or at least 3.9 Å) and / or at most 4.2 Å (e.g., at most 4.15 Å, at most 4.1 Å, at most 4.05 Å, or at most 4 Å). In some embodiments, at least 20% (e.g., at least 30%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 90%, at least 95%, or at least 99%) of the unit cells in the crystal structure comprise the above-described clusters (containing at least one alkali metal ion). In some embodiments, the above-described other anions and metal ions can be used in addition to the clusters to form the superconducting compound. For example, in addition to the clusters, a charge reservoir layer or doping mechanism (e.g., an interstitital ion) can be included to form the superconducting compound. 【0071】 Figure 1 shows a crystal structure including the above exemplary cluster (i.e., octahedral cluster) containing four in-plane ions and two buffer ions (e.g., alkali metal ions and alkaline earth metal ions or transition metal ions). As shown in Figure 1, the cluster includes anions 21, 22, 23, and 24 (e.g., O anions), transition metal ions 11, 12, 13, and 14 (e.g., Cu ions), and two buffer ions 31 and 32, at least one of which is an alkali metal ion (e.g., Li, Na, K, Rb, and Cs ions). Note that the halogen anions in the superconducting compounds described herein are not shown in Figure 1, and the atoms depicted in Figure 1 are for illustrative purposes only and not in exact ratios. Each of the transition metal ions 11, 12, 13, and 14 forms a covalent bond with neighboring anions. The transition metal ions 11, 12, 13, and 14 and the anions 21, 22, 23, and 24 form a plane, in which the metal ions 11, 12, 13, and 14 are located at the vertices of the plane and the anions 21, 22, 23, and 24 are located at the edges of the plane. The distance 34 or 35 between the buffer ion 31 or 32 and the plane is less than twice the radius of the buffer ion. In some embodiments, when the alkali metal ion 31 is the same as the alkali metal ion 32, the distance 34 is substantially the same as the distance 35. The distance between two opposing anions in the plane (i.e., the distance between anion 21 and 23, or the distance between anion 22 and 24) is 3.8 Å to 4.2 Å. In some embodiments, ion 31 is an alkali metal ion and ion 32 is a different ion (e.g., an alkaline earth metal ion or a transition metal ion). 【0072】 Figure 5 shows a representative crystal structure of a superconducting compound containing a halogen anion. Specifically, the crystal structure shown in Figure 5 includes alternating MA (e.g., CuO) layers and BA’ (e.g., NaCl) layers, where B, M, A, and A’ are defined above in relation to formula (I). As shown in Figure 5, the crystal structure includes anions 21, 22, 23, and 24 (e.g., O anions and / or halogen anions), transition metal ions 11, 12, 13, and 14 (e.g., Cu ions), two alkali metal ions 31 and 32 (e.g., ions of Li, Na, K, Rb, and Cs), and halogen anions 41, 42, 43, 51, 53, and 54. As shown in Figure 5, at least one vertex chalcogen anion (A) is replaced by a halogen anion (A’). 【0073】 In some embodiments, the superconducting compound of formula (I) may include clusters (e.g., subcell units in the crystal structure of the compound) having the formula BZMA2, BZMA2A’, B2MA2A’, BZ’MA2, or BZ’MA2A’. Here, B, Z, Z’, M, A, and A’ are defined above. 【0074】 Without being bound by theory, the clusters described herein (e.g., clusters having the structure of BZMA2, BZMA2A’, B2MA2A’, BZ’MA2, or BZ’MA2A’) are thought to primarily contribute to high Tc and superconducting activity / characteristics at high temperatures (e.g., at least about 150 K). Thus, without being bound by theory, all crystalline compounds having such clusters (e.g., metal oxide crystalline compounds) are thought to exhibit high Tc and superconducting activity / characteristics at high temperatures. 【0075】 In some embodiments, the superconducting compound described herein comprises at least 15% (e.g., at least 20%, at least 25%, at least 30%, at least 35%, at least 40%, at least 45%, at least 50%, at least 55%, at least 60%, at least 65%, at least 70%, at least 75%, at least 80%, at least 85%, at least 90%, at least 95%, at least 98%, at least 99%, or 100%) of the unit cells having the above clusters (e.g., as shown in FIG. 1) in its crystal structure. Without being bound by theory, superconducting compounds containing more of the above clusters (e.g., more than 50%) are thought to exhibit higher Tc based on the following model. In some embodiments, the superconducting compound described herein further contains one or more clusters similar to those shown in FIG. 1, except that the alkali metal ions are replaced by alkaline earth metal ions (e.g., Ca, Sr, or Ba) or rare earth metal ions (e.g., La). 【0076】 In some embodiments, the superconducting compound containing the above clusters may further contain transition metal ions or post-transition metal ions, such as the L ions in formula (I). Without being bound by theory, the additional anions attached to the L ions are considered as doping ions for the above clusters so as to make the plane formed by anions 21, 22, 23, and 24 conductive. Further, without being bound by theory, such a doping effect is thought to promote the formation of superconductivity in the compound. 【0077】 In some embodiments, the above-described cluster may have only two anions having a distance of 3.8 Å to 4.2 Å. In such embodiments, the other metal ions in the cluster may be located at any position in space to keep the two anions at the above distance. The reference to the plane formed by the anions 21, 22, 23, and 24 defined above is replaced by a line connecting these two anions. In some embodiments, a superconducting compound having such a cluster (e.g., a subcell unit in the crystal structure of a compound) may have the formula BMA2. Here, B, M, and A are defined above. 【0078】 In some embodiments, the superconducting compounds described herein are substantially pure. For example, the superconducting compound may have a purity of at least 50% (e.g., at least 60%, at least 70%, at least 80%, at least 90%, at least 95%, at least 98%, at least 99%, or 100%). 【0079】 Generally, the compounds described herein can become superconductors (e.g., capable of conducting superconducting current) at relatively high temperatures under atmospheric pressure. In some embodiments, the superconducting compounds described herein are superconductors at a temperature of at least 150 K (e.g., at least 160 K, at least 170 K, at least 180 K, at least 190 K, at least 200 K, at least 210 K, at least 220 K, at least 230 K, at least 240 K, at least 250 K, at least 260 K, at least 270 K, at least 273 K, at least 283 K, at least 293 K, at least 300 K, at least 320 K, at least 340 K, at least 360 K, at least 380 K, or at least 400 K), and / or at most about 500 K (e.g., at most about 480 K, at most about 460 K, at most about 450 K, at most about 440 K, at most about 420 K, or at most about 400 K). In some embodiments, the superconducting compounds described herein can have a Tc of at least 150 K (e.g., at least 160 K, at least 170 K, at least 180 K, at least 190 K, at least 200 K, at least 210 K, at least 220 K, at least 230 K, at least 240 K, at least 250 K, at least 260 K, at least 270 K, at least 273 K, at least 283 K, at least 293 K, at least 300 K, at least 320 K, at least 340 K, at least 360 K, at least 380 K, or at least 400 K), and / or at most 500 K (e.g., at most 480 K, at most 460 K, at most 450 K, at most 440 K, at most 420 K, or at most 400 K). Without being bound by theory, it is believed that the crystalline compounds having the above cluster structure can exhibit a high Tc based on the following model. 【0080】 In some embodiments, the present disclosure features a composition containing a superconducting compound described herein. In such embodiments, the composition can contain at least 1% (e.g., at least 2%, at least 3%, at least 5%, at least 10%, at least 20%, at least 30%, at least 40%, or at least 50%) and / or at most about 99.9% (e.g., at most 99%, at most 98%, at most 95%, at most 90%, at most 80%, at most 70%, at most 60%, or at most 50%) of the superconducting compound. 【0081】 In some embodiments, the present disclosure features a method for forming a superconducting compound. The method can include (1) mixing at least one metal oxide (e.g., a crystalline metal oxide) with at least a first and a second salt to form a mixture, where the metal oxide contains at least one transition metal or post-transition metal cation (e.g., Cu, Y, Bi cations), the first salt is an alkali metal halide salt containing an alkali metal cation (e.g., Li, Na, K, Rb, or Cs ions) and a halogen anion (e.g., F, Cl, Br, or I), and the second salt contains an alkaline earth or rare earth metal cation, and (2) sintering the mixture at a high temperature to form a crystalline compound containing alkali metal ions and halogen anions. In some embodiments, the atomic ratio of the alkali metal cation to the alkaline earth or rare earth metal cation is at least 1:1 (e.g., 2:1, 3:1, 5:1, or 10:1). In some embodiments, the at least one metal oxide can also contain an alkaline earth or rare earth metal cation. Examples of metal oxides that can be used as starting materials for preparing the superconducting compounds described herein include Y2O3, CuO, Bi2O3, CaO, BaO, and SrO. Examples of suitable alkali metal halide salts that can be used as starting materials for preparing the superconducting compounds described herein include KF, KCl, NaF, NaCl, RbF, RbCl, CsF, and CsCl. In some embodiments, the second salt contains an alkaline earth metal cation (e.g., Ca, Ba, or Sr cation) and at least one carbonate anion. Examples of such salts include CaCO3, BaCO3, and SrCO3. 【0082】 In some embodiments, the preparation method described herein comprises: (1) mixing at least one metal oxide (e.g., a crystalline metal oxide) with an alkali metal halide containing an alkali metal cation (e.g., Li, Na, K, Rb, or Cs ions) and a halogen anion (e.g., F, Cl, Br, or I) to form a mixture, wherein the at least one metal oxide contains at least one transition or post-transition metal ion (e.g., Cu, Y, or Bi ions) and at least one alkaline earth metal ion (e.g., Ca, Sr, or Ba ions), and the atomic ratio of the alkali metal cation to the at least one alkaline earth metal ion is at least 1:1; and (2) sintering the mixture at a high temperature to form a crystalline compound containing an alkali metal ion. Examples of suitable crystalline metal oxides that can be used as starting materials for preparing the superconducting compounds described herein include Bi2212, YBCO, Bi2223, Tl2212, Tl2223, Hg1201, Hg1212, and Hg1223. Thus, in some embodiments, the superconducting compound of formula (I) can be prepared by the above manufacturing method using the corresponding metal oxide and a suitable alkali metal halide (e.g., KF, KCl, NaF, NaCl, RbF, RbCl, CsF, or CsCl) as starting materials. 【0083】 In some embodiments, when the superconducting compound of formula (I) contains element D, element D can be introduced into the superconducting compound by adding a salt containing element D (for example, an alkali metal salt) to the mixture described in step (1) above. Suitable salts containing element D that can be used to prepare the superconducting compounds described herein include, for example, K2CO3, K2SiO3, K2B4O7, Rb2CO3, Rb2SiO3, Cs2CO3, Cs2SiO3, KHCO3, RbHCO3, or CsHCO3. For example, in order to prepare a superconducting compound of formula (I) containing element D which is carbon, an alkali metal salt containing carbon (for example, K2CO3, Rb2CO3, or Cs2CO3) can be used in step (1) above. In addition, the superconducting compounds described herein in which D is carbon can be prepared by sintering the crystalline metal oxide and the alkali metal salt under a CO2 stream to cause incorporation of carbon into the structure. It is believed that carbon atoms, when embedded in the crystal structure, can facilitate the incorporation of alkali metal ions in the crystal. 【0084】 In some embodiments, the atomic ratio (i.e., molar ratio) of the alkali metal ions in the alkali metal salt to at least one alkaline earth metal ion in the metal oxide is at least 1.3:1 (e.g., at least 1.5:1, at least 1.7:1, at least 2:1, at least 2.3:1, at least 2.5:1, at least 2.7:1, at least 3:1, at least 4:1, at least 5:1, at least 6:1, at least 7:1, at least 8:1, at least 9:1, at least 10:1, at least 11:1, at least 12:1, at least 13:1, at least 14:1, at least 15:1, or at least 16:1). In some embodiments, when the metal oxide starting material contains two or more alkaline earth metal ions, the above atomic ratio can be the ratio of the alkali metal ions in the alkali metal salt to one of the two or more alkaline earth metal ions in the metal oxide. Without being bound by theory, it is believed that by using an excessive amount (e.g., more than an atomic ratio of 1:1) of the alkali metal salt in the above method, the replacement of alkaline earth metal ions in the crystal structure of the metal oxide compound by alkali metal ions is promoted. Further, without being bound by theory, superconducting metal oxides containing a greater amount of alkali metal ions in the crystal structure are believed to exhibit a higher Tc based on the following model. 【0085】 Generally, the sintering temperature used in the above method may depend on various factors such as the structure of the synthesized compound and its melting temperature. In some embodiments, the sintering temperature is at least 300 °C (for example, at least 400 °C, at least 500 °C, at least 600 °C, at least 700 °C, at least 750 °C, or at least 800 °C), and / or at most 1200 °C (for example, at most 1100 °C, at most 1000 °C, at most 900 °C, at most 850 °C, at most 820 °C, or at most 800 °C). The sintering time (or the pressure holding time) can be at least 20 hours (for example, at least 30 hours, at least 40 hours, at least 50 hours, at least 100 hours, or at least 150 hours), and / or at most 300 hours (for example, at most 280 hours, at most 250 hours, at most 220 hours, at most 200 hours, or at most 150 hours). 【0086】 In some embodiments, the mixture of the crystalline metal oxide and the alkali metal salt can be sintered at a first temperature for a first period, and then sintered at a second temperature different from the first temperature for a second period. In some embodiments, the second temperature may be higher than the first temperature. The first or second temperature can be at least 750 °C (for example, at least 760 °C, at least 770 °C, at least 780 °C, at least 790 °C, at least 800 °C, or at least 810 °C), and / or at most 850 °C (for example, at most 840 °C, at most 830 °C, at most 820 °C, at most 810 °C, or at most 800 °C). 【0087】 In some embodiments, one or more layers of the superconducting compounds or their crystal structures described herein can be prepared using other methods known in the art such as pulsed laser deposition (PLD), atomic layer deposition (ALD), molecular beam epitaxy (MBE), and metalorganic chemical vapor deposition (MOCVD). An example of the MBE method that can be used to prepare the superconducting compounds described herein is described in WO2019 / 116103, the entire disclosure of which is incorporated herein by reference. For example, the superconducting compound BMAA’ (e.g., NaCuOF) described herein can be prepared using the PLD method or the MBE method known in the art. 【0088】 Without being bound by theory, the inventors believe that high-temperature superconducting compounds and methods of making such compounds are based on the principles and models described in more detail below. 【0089】 The superconducting behavior of charge carriers is thought to result from the near-degenerate dispersion relation ε(k) of the material near its Fermi level. Thus, while maintaining the connection between the prediction of superconducting behavior via the Schrodinger equation and the electronic and chemical structure of the corresponding material composition, the complete many-body Hamiltonian is simplified to a residual Hamiltonian that is formally similar to the reduced Hamiltonian assumed by the well-known BCS model [Bardeen, et. al., Phys. Rev. 108, 1175(1957)]. More specifically, the near-degenerate dispersion relation may be a result of the low overlap of electronic states. This enables the prediction of superconducting behavior as a result of the calculation of electronic states in small atomic clusters that provide a reasonable accuracy of meV (millielectronvolt). 【0090】 Thus, materials that are thought to impart superconducting behavior may be identified by using energy state calculations of at least two electronic states associated with the corresponding atomic clusters. Such atomic clusters generally include multiple atoms of at least one candidate element / species that are neutral atoms, cations, and anions. The calculations utilize geometric characterization of the atomic structure including distances between elements of the cluster. Note that the calculations may generally include variations in one or more ionic species and distances, which may suggest that certain atoms of the cluster are replaced by others. The frontier molecular orbitals of the cluster should be identified by appropriate calculations, and relatively low degeneracy frontier molecular orbitals may be detected. Frontier molecular orbitals generally relate to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). 【0091】 In addition, the band structure of a similar superconducting compound can be calculated to provide an estimate of the corresponding Fermi level. The atomic cluster may be varied such that the Fermi level is proximate to the energy level of the identified low degeneracy frontier molecular orbitals. 【0092】 Compounds described by the calculated atomic clusters may be determined to have a high probability of exhibiting superconducting behavior if the selected low degeneracy frontier molecular orbitals indicate that the bonding and antibonding energies differ by less than about 150 meV (e.g., less than 100 meV, or preferably less than 50 meV), and / or are greater than 1 meV (e.g., greater than 5 meV or greater than 10 meV). Typically, such atomic clusters have a high separation between adjacent energy levels. One should look for cases where the highest levels of the cluster, preferably the ground state and the first excited state, are essentially near degenerate. 【0093】 In some embodiments, the inventors believe that the following analysis provides a basis for identifying superconducting materials and methods of making such superconducting materials. See Gatt, Journal of Superconductivity and Novel Magnetism, 33, 1345. 【0094】 JPEG2025522476000002.jpg134166 【0095】 JPEG2025522476000003.jpg85166 【0096】 JPEG2025522476000004.jpg52166 【0097】 JPEG2025522476000005.jpg63166 【0098】 JPEG2025522476000006.jpg98166 【0099】 JPEG2025522476000007.jpg74166 【0100】 JPEG2025522476000008.jpg45166 【0101】 Therefore, the BCS theory is embedded in the stationary wave theory. The ground state becomes a condensate of non-dispersive stationary electron wave functions. The excited states are dispersive quasiparticle electron states (bogolons). Note that the electron operator c + and c in Equation (9) are understood as perturbative stationary wave states. 【0102】 In addition, the electrodynamic properties of superconducting materials can be derived from the London equations. According to the present disclosure, the London equations can provide a microscopic relationship between stationary electrons and the vector potential without requiring the rigidity of the many-body wave function. 【0103】 JPEG2025522476000009.jpg216166 【0104】 The Pippard integral appears as the sum of stationary wave states. To obtain the total current, the sum is taken over single-electron probability currents. Thus, the coherence length appears as the reciprocal of the sum of k-states in ρ2, which gives the non-local length scale over which the relationship between the current and the vector potential is maintained. According to Pippard, the coherence length gives an estimate of the critical temperature. Thus, the k-space extension of the flat-band region at the Fermi level gives an estimate of the critical temperature. A more accurate estimate of the critical temperature is obtained by estimating the low dispersion in k-space close to the Fermi level. This determines the parameter ρ2, and thus Δ and Tc. 【0105】 JPEG2025522476000010.jpg116166 【0106】 Thus, in the present disclosure, the rigidity of the many-body wave function maintained by the energy gap due to BCS treatment is replaced by the single-body relationship which is a property of any real wave function in the London gauge. Thus, the long-range coherence, described as the phase rigidity of the order parameter, can simply be understood as reflecting the single-electron behavior. 【0107】 Not bound by theory, the stationary wave theory is thought to provide an easy understanding of the gauge symmetry breaking observed in superconductors. This broken symmetry results from the breaking of the periodic boundary conditions of the electron wave function in the normal state, allowing any phase of the wave function. The stationary wave boundary conditions are generally obtained from the relaxation of the phonon cloud (or other bosons) for the stationary electron wave function (Equations 3 - 8) from the bulk. This is the proposed physical understanding of gauge symmetry breaking in the case of superconductivity. Grain boundaries and other defects only assist superconductivity by supporting these stationary wave states. 【0108】 JPEG2025522476000011.jpg54166 【0109】 JPEG2025522476000012.jpg40166 【0110】 As shown by Equation (23), in a superconductor, the surface current should be non-divergent, and the wave function ∇|Ψ(r,t)| = 0 should be null at the superconductor surface (in the London gauge). 【0111】 The understanding of the present disclosure may be derived from a quasiclassical perspective. Quasiclassically, a stationary wave is a beam of waves with a group velocity v g = 0. The magnetic force acting on such a beam of waves is F = v g × B = 0. Therefore, the quasiclassical stationary wave state is not affected by the magnetic field. However, as shown by the Aharonov - B effect, it is known that the vector potential action of the beam of waves affects the phase of the single - electron wave function. Thus, the superconducting current phenomenon acts not as a collective effect due to the coherence of the many - body wave function but simply as a phase current, which is the current of all the superconducting electrons as an appropriate beam of waves. Such a superconducting current does not interfere with electron - phonon relaxation and is a uniform current among all the superconducting electrons. 【0112】 The Pippard integral is derived from the relationship between the vector potential and the macroscopic current. To obtain the macroscopic current, an integral over all stationary wave k - states is required. This affects the real - space integral of the region on the order of the coherence length. 【0113】 As a result of the above understanding, the present disclosure provides a general rule for identifying new and improved superconducting materials. This is generally similar to the Wilson rule for metals and insulators. According to Wilson, a simple rule distinguishes insulating and conductive materials by positioning the Fermi level with respect to the energy band structure of the material. When the Fermi level cuts through the energy band, the material is a metal. When it is included in the gap, the material is an insulator. Also, when the gap is on the order of the thermal energy, the material is a semiconductor. 【0114】 Based on the above understanding, the present disclosure provides a general principle that when the Fermi level is close to a very shallow region of the energy level ε(k) (for example, at most 50 meV), the superconductor behaves as a metal. This condition is consistent with the above treatment of the kinetic energy term in Equation (9) as a perturbation. In addition, this also enables the above diagonalization of the Hamiltonian H0. Figures 2A - 2C schematically illustrate the relationship between the energy bands of the material, its Fermi level, and its corresponding conductance according to the Wilson rule and the present disclosure. 【0115】 In accordance with the above understanding, it is considered that the critical temperature for the superconducting effect (Tc) is determined by the size of the component ρ2(q), and thus by the expansion in k - space of the low - dispersion region ε(k). Equation (5) determines ρ2(q) as a three - dimensional sum in k - space for the states related to the processes of Equations (1) - (13). These are k - states that can be represented as perturbation stationary wave states in the normal state. These states constitute the low - dispersion region ε(k). This is consistent with the known measurements of superconductors by ARPES showing an extended low - dispersion region close to the Fermi level, as can be seen from Figures 3A - 3C showing known measured electronic structure results. 【0116】 Thus, the above general principle can identify new materials that can act as superconductors at a wide range of temperatures higher than existing superconducting materials. 【0117】 In addition, the general principle of the present disclosure provides superconducting materials that can exhibit superconducting behavior at a critical temperature higher than that of known materials. For example, the superconducting materials described herein may provide a Tc above 150 K, above 200 K, above 250 K, above 273 K, and around room temperature (about 300 K). 【0118】 As shown in the above equations (8) and (10), the energy gain in the superconducting state may be determined by the third term on the right side of equation (8). The critical temperature is determined by the energy gain. Since all other terms vary gently among materials in the same chemical family, the energy gain depends strongly on the square density term ρ2(q), as defined in equation (5). The magnitude of ρ2(q) is determined by the extent of the near-flat band in k-space. As an example, Figure 3B shows the results of angle-resolved photoemission measurements of some members of the cuprate family. As shown, the near-flat region extends over about 1 / 3 of the Brillouin zone. It is possible to expand this region. Thus, according to the present disclosure, the critical temperature can be raised by replacing the buffer ions in the cuprate structure (e.g., Bi2212 or YBCO) with alkali metal ions. These buffer ions control the dispersion ε(k), as shown below. 【0119】 More specifically, the technology of the present disclosure utilizes cluster calculations for the design of superconducting materials. In all synthetic superconductors to date having a critical temperature exceeding the boiling point of liquid nitrogen (77 K) at ambient pressure, at least one of the metal ions 11, 12, 13, and 14 in FIG. 5 is copper, all of the anions 21, 22, 23, and 24 in FIG. 5 are oxygen, the cations 31 and 32 are alkaline earth ions or rare earth ions, and all of the anions 41, 42, 43, and 44 (although not shown in FIG. 5, located at positions corresponding to anion 54) are oxygen. However, the present invention also includes other ion species in the plane defined by cations 31 and anions 41, 42, 43, and 44 and / or in the plane defined by cations 32 and anions 51, 52, 53, and 54 (52 is not shown in FIG. 5, located at the position corresponding to anion 42). In some embodiments, one or more of the anions 41, 42, 43, 44, 51, 52, 53, and 54 can be Group VII elements (e.g., fluorine F, chlorine Cl, bromine Br, or iodine I). Without being bound by theory, it is believed that these halogen anions can stabilize the alkali metal ions 31 and 32 and increase the critical temperature. In some embodiments, the anions 21, 22, 23, and 24 can be Group VI elements (e.g., oxygen O, sulfur S, selenium Se, or tellurium Te) or Group V elements (Group 15 elements) (e.g., nitrogen N, phosphorus P, or arsenide As). The reason for including such elements lies in their ability to generate near-bonding MOs (molecular orbitals) as follows using their p-orbitals. It is considered that these near-bonding MOs can be used to generate the near-flat electron bands necessary for superconductivity as described above. 【0120】 According to the present disclosure, accurate electronic state energy calculations can be performed on the octahedral structure shown in FIG. 1, which represents the material to be synthesized. The calculations are repeated at several representative values of distances 34 and 35 between metal ions 31 and 32 and the plane. These values are selected to be within the range predicted for the actual layered material, and in any case, for distance 34, it is between half of the ionic radius of metal ion 31 and twice the ionic radius of metal ion 31, and for distance 35, it is between half of the ionic radius of metal ion 32 and twice the ionic radius of metal ion 32. If metal ions 31 and 32 are the same, distances 34 and 35 are typically equal in each electronic state calculation. One criterion for superconductivity is that at least two of the electronic states of the octahedral structure, typically the ground state and the first excited state, are energetically close enough at some of the values of distances 34 and 35 to produce a near-flat dispersion as described above. Also, as described above, it is equally important to consider the structure of the highest occupied molecular orbital. 【0121】 When an octahedral structure satisfies a near-degenerate superconducting criterion (e.g., at most 50 meV between the ground state and the first excited state of a cluster) and proximity between the Fermi level and the corresponding energy band (e.g., at most 50 meV), the corresponding material is synthesized (e.g., using the methods described herein). Without being bound by theory, the inventors believe that the results of these calculations show a clear trend for cuprates, as shown in FIG. 4A. The data shown in FIG. 4A were collected from Panas et al., Chem. Phys. Lett, 259, 247. The most important among them is the effect of the ionic charge of the buffer ions. When the charge is small, the overlap decreases and a narrow-band dispersion results. Another less influential trend is the ionic radius of the buffer ions. When the ionic radius is large, the overlap decreases. The results of the quantum chemical calculations are reproduced in FIG. 4A. These results provide a clear synthetic route for the component ρ2(q). For example, as described above, it has been found that performing ion exchange using a precursor having an excessive amount of alkali metal ions is efficient for producing room-temperature superconductivity. In some embodiments, oxides and nitrates can be used as precursors. In some embodiments, when using a precursor containing a Group VI anion other than oxygen, the corresponding chalcogenide can be used. In some embodiments, an additional step of heating the sintered mixture in an oxygen atmosphere is necessary to provide interlayer oxygen for hole doping. In some embodiments, when the high-temperature superconductor contains mercury or thallium, special processing for synthesis may be required as known in the art. The superconductor can be synthesized by other methods known in the art, including laser beam ablation, sputtering, molecular beam epitaxy, or thin-film methods. In some embodiments, an artificial structure (superlattice) including the above-described cluster and the necessary charge reservoir layer or doping source can be obtained by the synthetic methods described herein. 【0122】 Based on the above principles and models, the present disclosure provides the following general requirements for identifying high-temperature superconductors: (1) Lower the dispersion region of ε(k) close to the Fermi level (e.g., less than 50 meV), that is, the energy difference between states in the cluster should be as small as possible; (2) The states in this low-dispersion region should preferably be coupled to phonons (or other bosons); (3) These electronic states should be delocalized. Note that surface states or local states do not contribute to superconductivity or contribute only limitedly and are nondispersive in the ARPES spectrum, giving the same effect. In addition, dispersive bands such as the Cu-O sigma band in cuprates provide screening of the Coulomb potential ν(q) in Equation (1) [Deutscher et al., Chinese Journal of Physics, 31, 805, (1993)]. 【0123】 Thus, the present disclosure provides a method for identifying a novel superconducting material based on the following steps: (1) Positioning the frontier molecular orbitals that are substantially non-bonding, which can be done by separating the anion atomic centers at an appropriate distance (e.g., 3.8 - 4.2 Å in cuprate compounds), and the molecular orbitals generally consist of p-orbitals extending in the space within the plane; (2) Positioning the frontier orbitals that are coupled to the vibrations of nearby metal ions approximating the plane. In this regard, the ionic charge of the metal ions approximating the plane is preferably selected such that the energy difference between the bonding and anti-bonding levels of the frontier orbitals is minimized. This energy difference is considered to determine the dispersion of a very narrow band. Based on appropriate cluster calculations, the ionic charge of the metal ions approximating the plane is preferably as small as possible. For example, in cuprate compounds (i.e., cuprates), the preferred ionic charge of the metal ions approximating the plane is +1 or less. In addition to the ionic charge, the radius of the metal ions approximating the plane in cuprate-based materials is also preferably high (such as the radius of K, Rb, or Cs). Thereby, the bonding-antibonding energy level separation can be reduced. This energy level separation determines the narrow band dispersion, and thus the size of the component ρ2(q). The size of the component ρ2(q) determines Tc. 【0124】 The table of FIG. 4B shows well-known representative HTS materials. Column 1 shows the ionic charge of the ions at the B site (i.e., the site corresponding to B in formula (I)). Column 2 shows the ionic radius of the ions at the B site. Column 3 shows the ionic charge of the ions at the Z site (i.e., the site corresponding to Z in formula (I)). Column 4 shows the ionic radius of the ions at the Z site. Column 5 shows the well-known compound name. Column 6 shows the number of CuO2 layers in the compound. Column 7 shows the Tc of different compounds. The above model can qualitatively explain the change in Tc of these compounds due to the effect of ionic charge and ionic radius on ρ2(q) as follows. The last compound is an exception to the rule and will be dealt with at the end of this paragraph. The effect of the number of CuO2 layers is obvious. With an increase in the number of layers, more k states are introduced into the sum (Equation 5), and ρ2(q) increases. This works as long as the doping mechanism is effective. An increase in the number of CuO2 layers also leads to an increase in the distance to the charge reservoir layer. The optimal condition is found for three layers. Therefore, a good comparison is made between compounds with the same number of layers. The first two rows of the table compare the single-layer compounds LBCO and Hg1201. The ionic charge at the B site drops from +3 in LBCO to +2 in Hg1201. The value of 2δ as an estimate of oxygen band dispersion drops from about 130 meV (calculated with scandium) to about 40 meV (calculated with calcium). This trend is obvious, and based on the above model, Tc increases by about a factor of 3, i.e., the factor of increase in ρ2(q). The next four rows compare bilayer compounds. From Bi2212 to YBCO, the ions at the B position increase their radius, and the ions at the Z position increase their charge. The B position is considered to dominantly affect ρ2(q). Therefore, Tc increases purely. However, based on the model described herein, a further increase in Tc is considered to be obtained by replacing the +3 ions at the Z position (Y) with +2 ions (Ca). This is shown in the next two rows showing Tl2212 and Hg1212. The advantage of the Hg compound over the Tl compound is due to the linear coordination of Hg that relaxes the structural strain. Next, three-layer compounds are shown. Bi2223 has three layers, but the ions at the B position are smaller.Therefore, the Tc increase is large for Bi2212, but not so for the bilayer Ba compounds Tl2212 and Hg1212. The same applies to the trilayer Tl compounds. The Tc increase is large for the bilayer compound Tl2212, but not so for the strain-relaxed Hg2212. The last trilayer compound Hg2223 seems to enjoy all the merits and consume all the merits of having +2 ions at the B and Z sites. The last line shows the properties of single-layer Bi2201. The relatively low Tc of this compound can be explained by the details of its Fermi surface and Fermi situation. 【0125】 Based on the above models and principles, the next step is to use +1 buffer ions with a large ionic radius at the B site. The 2δ value for using K+ instead of Ba++ as the buffer ion drops from about 40 meV to less than 5 meV. Therefore, the inventor believes that such materials can significantly increase Tc due to a large increase in ρ2(q). This increase is larger than the three-fold increase in Tc observed in 1987, due to the transition from +3 buffer ions at the B site to +2 buffer ions at the B site. The inventor believes that higher Tc can be obtained by transitioning to +1 ions at the B and Z sites for relaxation structures that purely contain +1 ions with a large ionic radius, such as HgCs2Na2Cu3O 6+δ or HgRb2Na2Cu3O 6+δ and so on. 【0126】 Thus, not being bound by theory, the above understanding of superconductivity leads to the inventors' idea that a certain material can exhibit superconducting behavior at relatively high temperatures (e.g., room temperature) under atmospheric pressure. For example, such a material has a crystal structure including copper oxide layers (i.e., cuprate layers), and alkali metal ions are located between or in proximity to the layers. In some embodiments, the fraction of alkali metal ions may be higher than 0.1 (e.g., higher than 0.2, higher than 0.3, higher than 0.4, higher than 0.5, higher than 0.6, higher than 0.7, higher than 0.8, higher than 0.9, or higher than 0.95) of the total amount of metal ions adjacent to the cuprate layers in the crystal structure of the superconductor compound described herein. 【0127】 In addition, the technology of the present disclosure provides a material containing negative ions (e.g., F - or O 2- ) located between at least some of the alkali metal ions and at least some of the metal oxide layers (e.g., the planes defined by anions 21-24 in FIG. 1). The negative ions provide further screening of the alkali metal ion charge, thus providing ions with an effective charge of less than +1 (e.g., at most 0.8, at most 0.6, at most 0.5, at most 0.4, at most 0.2, at most 0.1, or 0). 【0128】 In certain aspects, the present disclosure features an apparatus that is superconducting (e.g., exhibits superconducting properties such as conducting a superconducting current) at a temperature of at least 150 K (e.g., at least 180 K, at least 200 K, at least 230 K, at least 250 K, at least 273 K, at least 278 K, at least 283 K, at least 288 K, at least 293 K, at least 298 K, at least 300 K, at least 305 K, or at least 310 K) under atmospheric pressure. Exemplary apparatuses include cables, magnets, levitation devices, superconducting quantum interference devices (SQUIDs), bolometers, thin film devices, motors, generators, current limiters, superconducting magnetic energy storage (SMES) devices, quantum computers, communication devices, high-speed single flux quantum devices, magnetic confinement fusion reactors, beam steering and confinement magnets (such as those used in particle accelerators), RF and microwave filters, and particle detectors. 【0129】 Among the other use cases described above, the superconducting compounds described in the above and following examples are useful in fault current limiting (FCL) devices. An FCL is a device that limits the predicted fault current without completely disconnecting when a fault occurs (e.g., in a power transmission network). Power distribution systems typically include circuit breakers for disconnecting power during a fault, but to maximize reliability, it is desirable to keep the disconnected portion of the network as small as possible. This means that even the smallest circuit breaker and all the wiring connected to it must be able to interrupt a large fault current. 【0130】 Referring to FIG. 6, the main function of the FCL device 610 is to limit the flow of current to a predetermined safe level and prevent excessive current from flowing through a system such as the power transmission network 600. By limiting the fault current, the FCL device 610 protects equipment, reduces stress on electrical components such as the computer server 620 that draws power from the network 600, and enhances the overall stability of the system. 【0131】 The FCL device 610 is a non-linear element with low impedance at normal current levels but high impedance at fault current levels. Furthermore, this change is very rapid, and the circuit breaker operates after a few milliseconds. During a fault, the power is unstable, but it is not completely disconnected from the network. After the branch of the faulty distribution network is disconnected and the current returns to normal levels, the fault current limiter (FCL) automatically returns to normal operation. 【0132】 Superconducting fault current limiters utilize the fact that superconductivity is extremely rapidly lost ( "quenching") when the critical temperature, critical current density, and / or critical magnetic field strength are exceeded. In normal operation, current flows through the superconductor with zero or near-zero resistance and negligible impedance. When a fault occurs, the superconductor quenches, its resistance rises rapidly, and the current is diverted to a parallel circuit with a desirable high impedance. 【0133】 Generally, superconducting FCL devices include resistive devices and inductive devices. Generally, the selection of a fault current limiter varies depending on various factors such as specific applications, system requirements, budget constraints, etc. FCL plays an important role in maintaining the reliability and safety of the power system by reducing the impact of fault currents and preventing damage to equipment and infrastructure. 【0134】 As shown in FIG. 7, an example of a resistive FCL device 700 includes a superconducting electrical conduction element 710 connected in parallel with a resistor 750. Element 710 includes a superconducting wire 720 extending between two electrical contacts 730. A heat sink 740 is arranged to be in thermal contact with the superconducting wire 720. The heat sink is formed from a material having a thermal conductivity sufficient to rapidly conduct heat away from the superconducting wire 720. 【0135】 The element 710 is designed to provide sufficient superconducting current capacity, and during the normal operation of the device 700, the current directly passes through the element 710 in the superconducting state. However, the element 210 has a current threshold beyond which it quenches. For example, when quenched by a fault current, the resistance rapidly increases and the fault current decreases from the original fault current (predicted fault current). The device 700 can be designed according to a desired current threshold depending on the application in which the device is used. 【0136】 Examples of the resistive FCL element 800 are shown in FIGS. 8A - 8C. The element 800 includes a plurality of strips 810 of superconducting material extending between two electrical contacts 830. The strips 810 are separated by an electrical insulating material and, under normal operating conditions (below Tc, below the critical current of the superconducting strip), each provides a parallel superconducting electrical connection between the contacts 830. Each contact 830 is integrated with an electrical contact pad 840 that bolts the element 800 to an electrical transmission line or other component of an electrical circuit. The contacts 830 and pads 840 are formed from a conductive material such as copper. 【0137】 The strips 810 are disposed between two sapphire plates 820 that function as a heat sink for the element. The material between the strips may also be sapphire. An additional outer layer 850 can also be included. In some cases, these layers can be a conductive material such as copper. In certain examples, these layers can operate as ohmic conductors that conduct current when the fault current threshold is exceeded. In some examples, these layers can be protective layers. 【0138】 Generally, the dimensions of the device, the number of superconducting strips, and other parameters can be selected based on the use case of the FCL. By stacking and connecting in parallel a plurality of such elements, a larger capacity than a single element can be achieved. 【0139】 The threshold current of the superconducting compound useful for such an FCL device can be set based on the current-voltage characteristics of the material or device. An example of the current-voltage curve of the superconducting material is shown in FIG. 9A. Such an example of the curve for a specific compound sample will be further described in the examples below. The current-voltage curve obtained at a fixed temperature below Tc shows a sharp transition from the superconducting state to the normal conducting state at the threshold current. This transition indicates that the resistance of the test sample has increased significantly. 【0140】 The threshold current during the transition and the steepness of the I-V curve can vary depending on the device and its operating temperature. For example, FIG. 9B shows the I-V curves of device examples at four different temperatures across Tc, citing a paper by Professor A. Campbell of the University of Cambridge. At 300K, which is lower than Tc at the lowest operating temperature shown in this graph, the transition starts at a current IR > 0 amperes and increases monotonically with the increase in current. At 330K, the transition starts at a lower current, follows an S-shaped transition, and increases more rapidly than the 300K curve. Here, the same current value as the 300K curve is obtained at a significantly higher voltage (which indicates an increase in resistance). At 350K, although the transition from superconducting to normal conducting is still evident at a temperature lower than Tc, the threshold current is lower than that at 330K. The device resistance at this temperature is still higher than that at 330K for the same current. Finally, the I-V curve at 360K is linear and corresponds to an ohmic conductor, indicating that the device is no longer superconducting. 【0141】 In a resistive FCL device, even with a heat sink, the onset of the transition from superconducting to normal conducting can cause the superconductor to be heated significantly and rapidly, and the resistance of the sample may increase. Such behavior is advantageous in an FCL where it is necessary to rapidly increase the impedance of the circuit so that the device is not exposed to the fault current. 【0142】 Generally, a resistive FCL device can be either DC or AC. In the case of AC, it can result in stable power dissipation from the AC losses (superconducting hysteresis losses) removed by the heat sink 240. 【0143】 Referring to FIG. 10, the inductive FCL device 1000 is generally designed as a transformer having a resistive FCL as the secondary coil 1010 (e.g., having a core). The secondary coil 1010 is inductively coupled to the primary coil 1010 connected in series to the transmission line. In normal operation without a fault, since the resistance of the secondary coil 1010 is little or none, the inductance of the device is low. Due to the fault current in the primary coil, a current is induced in the secondary coil, quenching the superconductor, so that the secondary coil 1010 becomes resistive and the inductance of the whole device increases. The advantage of this design is that heat does not penetrate into the superconductor through the current leads, so the cryogenic power load may be low. 【0144】 Examples of superconducting secondary coils 1100 for inductive FCL devices are shown in FIGS. 11A - 11C. The secondary coil 1100 includes a wound coil 1110 and a core 1120 (or other ferromagnetic material). The coil 1110 includes a bulk cylinder of superconducting wire 1116 within a sapphire cylinder 1114. The outer coil of copper wire 1112 is wound around the sapphire cylinder 1114. In this example, the core 1120 is a closed core. In other examples, it may be an open core. 【0145】 The FCLs in the above examples operate at room temperature and do not include cryogens to maintain the superconducting state, but other implementations are possible. For example, any of the above examples can optionally include a cooling system to maintain the temperature of the superconducting element below a threshold temperature. The cooling system may include a coolant such as water, oil, or a cryogen such as liquid nitrogen. 【0146】 Figure 12 shows an example of an FCL system 1200 including a cooling system. Here, the system 1200 includes the above-described FCL device 700 connected to a cooling subsystem 1210. The system 1200 includes a cryostat 1220 that houses the superconducting element 710. The cooling subsystem 1210 is connected to the cryostat 1220 via a conduit 1230 that guides a coolant from the subsystem 1210 to the cryostat. The coolant maintains the temperature of the superconducting material in the element 710 below the critical temperature of the superconducting material and enables the element 710 to conduct current in normal current conduction. In some examples, the cooling system 1210 can variably control the temperature of the superconducting material to change the threshold current of the FCL device 700. 【0147】 In the superconducting FCL of each of the above examples, the superconducting material may include one or more of the superconducting materials described in the above and following examples. Generally, the critical temperature of the superconducting FCL device is 200 K or higher (e.g., 250 K or higher, 300 K or higher, 350 K or higher). The critical current of the superconducting FCL device varies depending on the application and can be in the range of 1 ampere (A) to 100 kA (e.g., in the range of 10 A to 100 A, 100 A to 1 kA, 1 kA to 100 kA). The advantage of the FCL device described herein is that the device can be adjusted to an appropriate critical current according to the specific use case of the FCL device. Thus, for example, a high-voltage network operating at high voltage and low current can utilize an FCL device having a first critical current, while other applications such as a data center operating at low voltage (e.g., 400 V) and high current (e.g., 20 kA) can utilize another FCL device having a different (e.g., higher) critical current. 【0148】 The entire contents of all publications (e.g., patents, patent application publications, articles) cited herein are hereby incorporated by reference. 【0149】 General description of synthesis and characterization of high-temperature superconductors As described in this specification, the chemical composition of the compounds described in the examples was measured by energy-dispersive spectroscopy (EDS). The Tc of the compounds described in the examples was measured by the four-probe method [Low Level Measurements Handbook, 6th edition, Keithley]. The transport measurements were carried out using a Quantum Design PPMS system at the University of Zaragoza (UNIZAR), or a Keithley 2450 source measurement unit (SMU) and a Keithley 2430 SMU. The magnetic measurements were carried out using a Quantum Design MPMS system at UNIZAR or the Weizmann Institute of Science (WIS). 【0150】 The following families of compounds derived from the above models were synthesized and showed room-temperature superconductivity properties: YBCO and BSCCO modified to contain alkali metal ions (e.g., K or Rb) and halogen anions (e.g., F). 【0151】 Various compounds belonging to the above family were synthesized by the following general procedure: For YBCO, the stoichiometric amounts of CuO, BaCO3, KF or RbF, and Y2O3 were ground, pressed, and sintered at 700 - 850 °C for 24 - 72 hours to prepare Y(K x Ba 1-x ) r Cu p O y F s or Y(Rb x Ba 1-x ) r Cu p O y F s where x is 0.2 - 1, r is 1 - 5, p is 1 - 4, y is 3 - 7, and s is 0.3 - 4. For BSCCO, the stoichiometric amounts of CuO, Bi2O3, RbF, SrCO3 and CaCO3 were sintered at 690 - 820 °C for 24 - 96 hours to prepare Bi n (Rb x Sr 1-x ) r Ca p-1 Cu p O y Fs was prepared. Here, n is 2 - 4, x is 0.2 - 1, r is 1 - 3, p is 0 - 3, y is 6 - 18, and s is 0.3 - 2. 【0152】 Furthermore, in some cases, the reaction was carried out in 1 - 5 stages of grinding, pressing, and sintering. In most cases, the mixture was ground in a glove box filled with an inert atmosphere such as Ar or N2, pressed inside the glove box, and sintered in an inert atmosphere at 690 - 810 °C. Modifications to this general procedure are described in detail in the examples. In some implementations, the sintering temperature is 680 °C - 750 °C. The sintering temperature range described herein can, in some cases, provide a useful balance between a temperature that is not too high (e.g., leading to melting or formation of undesirable compounds) and a temperature that is not too low (e.g., providing a high - purity composition). 【0153】 Also, in some cases, these temperature ranges are lower than the temperatures normally used to process YBCO / BSCCO compounds because the presence of alkali metals in the modified compounds can potentially suppress the melting temperature. For example, in some implementations, the sintering temperature is 900 °C or lower, 875 °C or lower, or 850 °C or lower, and these temperature ranges can reduce (e.g., suppress) melting. 【0154】 Treatment in an inert atmosphere is recognized as useful for the synthesis of the described compounds containing halogens such as F for the purposes of the present disclosure. Halogens react strongly with water vapor in the atmosphere and can interfere with the synthesis of these compounds. The inert atmosphere promotes the high - purity synthesis of these compounds, resulting in a more uniform form and / or a higher superconducting critical temperature. 【0155】 In some implementations, after at least one sintering cycle, the sintered composition is heated in an oxygen atmosphere to provide inter - lattice oxygen and / or structural oxygen for hole doping. Doping can increase the conductivity and / or Tc. 【0156】 In some implementations, the sintered composition is purified by a micro-pulling down (μ-PD) crystal growth process. In the μ-PD process, the sintered composition (e.g., any one of Compounds 1 to 7 described below) is melted in a crucible and transported through microchannels / capillaries created at the bottom of the crucible. Continuous solidification of the melt proceeds at the liquid / solid interface disposed below the crucible, forming high-purity crystals. Since the compounds described herein contain halogens, this process is carried out in an inert atmosphere. 【0157】 For example, as shown in FIG. 13, the μ-PD apparatus 1300 includes a sealed chamber 1302 made of stainless steel and / or glass. To facilitate maintaining an inert atmosphere within the chamber 1302, the μ-PD apparatus 1300 includes a gas inlet 1304 (e.g., for the inflow of nitrogen and / or argon) and a gas outlet 1306 (e.g., fluidly connected to a pump). 【0158】 The heated crucible 1308 is within the chamber 1302 and holds the sintered composition 1310. The crucible 1308 can be, for example, a platinum crucible, or a crucible or other material capable of withstanding the temperature used to melt the sintered composition 1310. The sintered composition 1310 is melted (e.g., at a temperature in the range of 800 °C to 1,000 °C depending on the composition) and passes through the micro nozzle 1320. The flow of the molten sintered composition contacts the seed crystal 1314, and the grown crystal 1312 is formed based on the crystal structure of the seed crystal 1314. For example, the meniscus of the molten sintered composition is formed at the orifice of the micro nozzle 1320, and the seed crystal 1314 can be initially placed in contact with the meniscus and arranged to form a liquid / solid interface at the bottom of the orifice. The seed crystal 1314 can be an oriented bar cut from a previous growth of the same or similar composition, a crystal of the same or similar composition obtained by μ-PD or other methods, or a different isostructural crystal having a melting point higher than that of the molten sintered composition. In some implementations, an after heater 1316 (e.g., a heating coil such as a platinum wire) is arranged adjacent to the flow of the molten sintered composition and is controlled to provide a temperature gradient adjustable along the growth direction and / or the axial direction. In some implementations, the longitudinal temperature gradient along the growth direction is 10 °C / mm to 100 °C / mm. In some implementations, the axial temperature gradient is 100 °C / mm to 300 °C / mm. This temperature has been observed to result in highly pure crystalline fibers with few or no crystal defects or new crystal defects. 【0159】 During crystal growth, the seed crystal 1314 is moved downward relative to the melt of the crucible 1308 / sintered composition 1310 within the chamber a02 using, for example, a control arm, an actuator, a moving platform, an elevator, or other moving mechanism 1318 configured to move the seed crystal 1314 downward. In some implementations, the moving speed is from 0.2 mm / min to 2.0 mm / min. This speed has been observed to result in high-quality crystals. Thus, the length of the grown crystal 1312 gradually increases. After the crystal has grown to the desired length, the grown crystal 1312 is cooled, for example, to room temperature. 【0160】 The length of the solute diffusion boundary layer can be controlled by adjusting the length of the micro-nozzle 1320 with little or no convection. In some implementations, the length of the diffusion layer in stable growth is set to about 100 μm. Further, the crystal growth rate can be 2 ~10 3 multiplied by 10. As a result, a compositionally homogeneous crystal of the superconducting compound described herein grows as compared to the results obtained by other crystal growth methods (e.g., segregation coefficient Keff is about 1). 【0161】 No voids or dislocations appeared in the fiber crystals grown in such a manner. It is considered that the generation of dislocations was suppressed by the very stable linear radial temperature distribution in the growth region. 【0162】 By using an apparatus such as the apparatus 1300 in which the movement of the seed crystal and crystal growth are performed in an inert atmosphere within a sealed chamber, alkali ions and halogen ions can be included in the crystal. 【0163】 In some implementations, the crystal grows as a fiber. Fibers grown according to the methods described above have a uniform diameter, are crack-free, and are composed of plate-like crystals, and have been observed to exhibit superconductivity, for example, at high temperatures. For example, FIGS. 14A-14B show examples of fibers having lengths of approximately 3 cm and approximately 6 cm, respectively. The fibers were grown by sintering a mixture to obtain BSCCO and then melting and recrystallizing the BSCCO using μ-PD as shown in FIG. 13. The fibers have a generally uniform morphology along their length, reflecting their homogeneous composition. This homogeneity is shown in FIGS. 15A-15B. FIG. 15A is an SEM micrograph of the sintered BSCCO compound 1500 before melting and recrystallization using μ-PD, and FIG. 15B is an SEM micrograph of the BSCCO compound 1506 after μ-PD. The compound 1500 is very heterogeneous at the microscopic level shown. For example, the compound 1500 has O% = 41, Ca% = 9, Cu% = 13, Sr% = 11, and Bi% = 26 at position 1502, but is CuO at position 1504. The sintered BSCCO compound was found to be approximately 50% pure (a 50% composition of Bi2212 or Bi2201). On the other hand, the BSCCO compound synthesized additionally using μ-PD has a purity greater than 90%, and the composition of region 1508 of compound 1506 was found to be O% = 49, Ca% = 6, Cu% = 12, Sr% = 14, and Bi% = 19. 【0164】 Magnetic measurements have shown that μ-PD processed compounds have intergrowth of Bi2201 and Bi2212. For example, as shown in FIG. 16 (showing the magnetic moment of the sample as a function of temperature using a SQUID magnetometer), the two marked peaks / transitions indicate the presence of Bi2201 and Bi2212 in the same sample, with Bi2201 occupying most of the sample. This effect has been observed in both compositions containing halogen anions and alkali metal ions and samples that do not contain them. For example, as shown in FIG. 17, when measured under the condition of H = 100 Oe, the sintered BCBO composition modified with Rb and F inclusions showed two marked peaks corresponding to the Bi2201 and Bi2212 parts and a low-T transition associated with doped Bi2212. 【0165】 For the purposes of the present disclosure, it has been recognized that the proportion of Bi2212 in the synthesized material can be a target parameter to be adjusted in order to improve the performance of the material. For example, in some cases, Bi2212 is associated with a higher superconducting transition temperature than other phases (e.g., Bi2201), and increasing the Bi2212% can provide a higher critical current and / or critical magnetic field at high temperatures. In some implementations, the Bi2212% can be at least partially determined by one or more processing temperatures (sintering temperature, recrystallization temperature, or both) of the composition. This effect is sensitive, and it has been observed that a small difference in temperature (e.g., less than 20 °C) can cause a large change in the Bi2212% of the sintered composition and the fibers obtained from μ-PD. For example, in some implementations, the Bi2212% is at least 50%, at least 75%, or at least 90%. 【0166】 The use of μ-PD is not limited to a specific example of the Bi2212 compound. Other types of superconducting compounds within the scope of this disclosure, such as YBCO, Bi2223, Tl2212, Tl2223, Hg1201, Hg1212, and Hg1223, can also be processed using μ-PD to obtain some or all of the advantages described for Bi2212. For example, the purity of the fibers formed by these processes (volume% of modified YBCO, modified Bi2223, etc. within the fibers) will be at least 90%. 【0167】 The following examples are illustrative and not limiting. [Examples] 【Examples】 【0168】 Synthesis and Characterization of Superconducting Compounds 1-3 Bi2O3, CuO, RbF, SrCO3, and CaCO3 were weighed according to the following three compositional formulas: Bi2Rb 1.2 Sr 0.8 CaCu2O x F 1.4 (Compound 1 or B2B60), Bi2Rb 1.4 Sr 0.6 CaCu2O x F 1.4 (Compound 2 or B2B70), and Bi2Rb 0.8 Sr 0.6 Ca 0.6 CuO x F 1.4 (Compound 3 or B1BC40). The powders were pelletized at a pressure of 4000 kg / cm 2 at room temperature and then milled in a ball mill at 750 RPM for 5 hours. In the following sintering cycle procedure, round pellets (average diameter 7 mm) were used. For the final electrical measurements, square pellets (8 mm) were pressed and sintered. This procedure was carried out within a glove box filled with an inert atmosphere of nitrogen. 【0169】 The sintering procedure was carried out in a furnace at 710 °C for B2B70 and B2B60, and at 690 °C for B1BC40. Each cycle of the heat treatment included heating the sample from 200 °C to the target temperature at a heating rate of 5 °C / min and holding the sample at the target temperature for a total of 12 hours. At the end of each heat treatment, the sample was cooled to 200 °C in the furnace. The cooling took several hours without controlling the cooling rate. The above sintering cycle was performed a predetermined number of times (e.g., 3 or 4 times) for each sample. After the sintering cycle, each batch of pellets was repulverized and pelletized in a glove box. 【0170】 The samples were investigated by SEM observation, EDS analysis, and X-ray powder diffraction (XRPD). SEM micrographs and EDS analysis were performed with a Thermo Fisher Phenom ProX G6 Desktop SEM. Phase analysis of the samples was carried out by the XRPD method. Data were collected with a Panalytical Empyrean powder diffractometer (Kα radiation, λ = 1.541 Å) equipped with an X’Celerator linear detector and operating at v = 40 kV and I = 30 mA. All the measurements described in this specification were performed under ambient pressure. 【0171】 Electrical measurements were performed by the standard four-probe continuous DC method using an interactive digital source meter Keithley 2450 SMU and Keithley 2430 SMU. 【0172】 Several configurations for assembling the contacts for electrical measurements were developed as follows. 【0173】 (1) Four indium contacts were gently pressed onto the pellet. A solid-core Cu wire was attached to the indium contacts using silver paste. The sample and the entire base were covered with a dielectric coating and dried on a hot plate at 120 °C for 20 minutes. The coating procedure was repeated twice to ensure the sample was securely blocked from air. 【0174】 (2) Four indium contacts were pressed onto a 10 mm silicon wafer. Cu wires were attached to the indium contacts using silver epoxy. A rectangular pellet was attached to the indium contacts using drops of silver epoxy. This procedure was carried out on a hot plate at 130 °C. Subsequently, the device was cured for 1 hour. A dielectric coating was applied in the same manner as the previous configuration. To completely seal the device and ensure an inert atmosphere, the device was sealed in a designated package. The sealing was performed by an arc welding procedure inside a glove box. 【0175】 (3) To improve the contact between indium and the sample, a new configuration using a printed circuit board (PCB) was developed. In this method, the PCB was designed with a gold mask designated for indium contacts on top. After soldering indium wires onto the gold mask, Cu wires were soldered at the designated positions. Next, the pellet was placed on the contacts and pressed with a second similar PCB using four screws. A dielectric coating was applied in the same manner as the previous configuration (3 hours, 120 °C), except that a longer hanging time was required on the heating plate due to the shape of the device. Due to the shape of the new PCB device, an airtight sealing package was used. All compounds were measured with this configuration. 【0176】 (4) In some implementations, contacts are formed by diffusing silver into the synthesized composition at high temperature. This allows the production of ohmic contacts rather than blocking Schottky contacts. 【0177】 Results The superconducting compound 1 (B2B60) was prepared according to the above procedure. The composition of Compound 1 was measured by EDS at four locations (spots) on the sample. The results are summarized in Table 1 below. In this specification, the unit "at%" refers to atomic percentage. As shown in Table 1, the atomic fraction suggests that Compound 1 has the formula: Bi2(Sr, Rb, Ca)2CuO y F s and has. 【0178】 【Table 1】 【0179】 Magnetic measurements of Compound 1 were carried out. The results are shown in Fig. 18. Based on Fig. 18, the critical temperature (Tc) of Compound 1 is estimated to exceed 400 K. 【0180】 Fig. 19 shows the resistance as a function of current for the pristine (original state) Bi2212 material obtained by four-probe electrical measurement. The resistance saturates at about 4.5 ohms at 20 °C under ambient pressure. 【0181】 Fig. 20 shows similar four-probe electrical measurements for B2B60 (Compound 1) obtained above using the second configuration under the same conditions and with the same form factor. As shown in Fig. 20, the resistance saturated at about 10^-5 ohms at 293 K under ambient pressure. Based on the negligible resistance shown in Fig. 20, the critical temperature of B2B60 is estimated to exceed 293 K. Without being bound by theory, the relatively high resistance at low current is thought to be caused by incomplete electrical contact. 【0182】 Magnetic measurements of Compound 1 were carried out. The results are shown in Fig. 21. As shown in Fig. 21, when measured at a magnetic field strength of 1 T, Compound 1 shows a hysteresis effect in magnetic measurements between zero-field cooling (ZFC) measurement (lower curve) and field cooling (FC) measurement (upper curve), which is consistent with the behavior of superconducting compounds. 【0183】 Superconducting Compound 2 (B2B70) was prepared according to the above procedure. The composition of Compound 2 was measured by EDS at three spots on the sample. The results are summarized in Table 2 below. As shown in Table 2, the atomic fractions suggest that Compound 2 has the formula: Bi2(Sr, Rb, Ca)2CuO y F s and. 【0184】 【Table 2】 【0185】 Figure 22 shows similar four-probe electrical measurements of B2B70 (Compound 2) under the same conditions and with the same form factor. As shown in Figure 22, the resistance saturated at about 8×10^−5 ohms at 293 K under ambient pressure. Based on the negligible resistance shown in Figure 22, the critical temperature of B2B70 is estimated to exceed 293 K. 【0186】 Figures 23A - C show four-probe electrical measurements of B2B70 under the same conditions and with the same form factor. The sample shown in Figure 23A was obtained by performing 6 sintering cycles, the sample shown in Figure 23B was obtained by performing 4 sintering cycles, and the sample shown in Figure 23C was obtained by performing 5 sintering cycles. For the samples shown in Figures 23A - B, the contacts were made using the above-described first configuration. For the sample shown in Figure 23C, the contacts were made using the above-described second configuration. As shown in Figures 23A - C, the voltage of B2B70 rapidly increased at the critical current. This can be used for use in an FCL device as described above. 【0187】 The resistance measured as a function of current for a sample of B2B70 (Compound 2) is shown in Figure 24A. The measurement was performed at a temperature of 75 °C. After the resistance of the sample increased rapidly, the resistance was negligible for currents up to about 0.55 A. This behavior is characteristic of a superconducting material at currents below the critical current of the sample. 【0188】 XRD analysis of Compound 2 was performed. The results are shown in Figure 24. The Rietveld refinement converged with Ri = 3.5%. In Figure 24B, the peaks of modified Bi2212 were identified, and the remaining peaks marked with circles are the peaks of modified Bi2201. As shown in Figure 24B, most of the obtained structure was modified Bi2201, but a small amount of modified Bi2212 was identified. The small amount (about 3.5%) of modified Bi2212 is considered to be the cause of the observed room-temperature superconductivity. The major phase (50%) of modified Bi2201 is considered to be a superconductor with a lower Tc. The synthesis temperature is considered to be a determining factor in increasing the proportion of modified Bi2212 at the expense of modified Bi2201. 【0189】 The superconducting compound 3 (B1BC40) was prepared according to the above procedure. The composition of compound 3 was measured by EDS at two locations (spots) on the sample. The results are summarized in Table 3 below. As shown in Table 3, the atomic fraction suggests that compound 3 has the formula: Bi2(Sr, Rb, Ca) 1.5 CuO y F s which suggests that it has the formula: Bi2(Sr, Rb, Ca)CuO 【0190】 【Table 3】 【Example】 【0191】 Characteristic evaluation of superconducting compound 4 The superconducting compound 4 was prepared according to the above procedure, except that sintering was continued at 750 °C for 48 hours. The composition of compound 4 was measured by EDS. The results are summarized in Table 4 below. As shown in Table 4, the atomic fraction suggests that compound 4 has the formula: YRb3CuO 1.5 F3 which suggests that it has the formula: YRb3CuO 【0192】 【Table 4】 【0193】 Magnetic measurements of compound 4 were carried out. The results are shown in Figure 25. As shown in Figure 25, when measured at 1 T, compound 4 showed a hysteresis effect in the magnetic measurement between the zero-field cooling (ZFC) measurement (lower curve) and the field cooling (FC) measurement, indicating superconducting properties. Also, based on Figure 25, the critical temperature (Tc) of compound 4 is estimated to be about 500 K. 【Example】 【0194】 Characteristic evaluation of superconducting compound 5 The superconducting compound 5 was prepared according to the above procedure, except that sintering was carried out at 750 °C for 24 hours. Thereafter, the sample was slowly cooled to 200 °C. The composition of compound 5 was measured by EDS. The results are summarized in Table 5 below. As shown in Table 5, the atomic fractions suggest that compound 5 has the formula: Bi2SrRb 1.5 Ca 0.5 Cu 1.5 O 17 F. This formula suggests the intergrowth of the Rb-2212 phase and the Rb-2201 phase, as also shown by XRD and magnetic measurements. 【0195】 【Table 5】 【0196】 Magnetic measurements of compound 5 were performed. The results are shown in Figure 26. As shown in Figure 26, when measured at a magnetic field strength of 1 T, compound 5 showed a hysteresis effect in the magnetic measurements between the zero-field cooling (ZFC) measurement (lower curve) and the field-cooling (FC) measurement (upper curve), indicating superconducting properties. Also, based on Figure 26, the critical temperature (Tc) of compound 5 is estimated to be about 500 K. 【Example】 【0197】 Characteristic evaluation of superconducting compound 6 The superconducting compound 6 was prepared according to the above procedure, except that the sintering cycle was performed 3 times, with the first cycle sintering carried out at 720 °C for 48 hours, the second cycle sintering at 720 °C for 16 hours, and the third cycle sintering at 720 °C for 19 hours. The composition of compound 6 was measured by EDS. The results are summarized in Table 6 below. As shown in Table 6, the atomic fractions suggest that compound 6 has the formula: Bi2Sr 0.7 Rb 0.65 CaCu 1.5 O 11 F. Similar to compound 5, this formula suggests the intergrowth of the Rb-2212 phase and the Rb-2201 phase. 【0198】 【Table 6】 【Example】 【0199】 Characteristic Evaluation of Superconducting Compound 7 Superconducting compound 6 was prepared according to the above procedure, except that the sintering cycle was performed 3 times, the sintering in the first cycle was carried out at 750 °C for 96 hours, the sintering in the second cycle was carried out at 750 °C for 24 hours, and the sintering in the third cycle was carried out at 750 °C for 72 hours. The composition of compound 7 was measured by EDS. The results are summarized in Table 7 below. As shown in Table 7, the atomic fraction indicates that compound 7 has the formula: Bi2Sr 0.75 Rb 0.75 Ca 1.2 Cu 1.2 suggests having O7F1. 【0200】 【Table 7】 【0201】 Other embodiments are within the scope of the following claims.

Claims

[Claim 1] Equation (I): L ｎ D ｍ (B ｘ B’ １－ｘ ) ｒ (Z ｔ Z’ １－ｔ ) ｑ M ｐ A ｙ A’ ｓ (I) A compound of, n is a number between 0 and 3. m is a number between 0 and 6. x is a number between 0.1 and 1. r is a number between 1 and 8. t is a number between 0 and 1. q is a number between 0 and 6. p is a number from 1 to 7. s is a number between 0 and 20. y is a number between 0 and 20. L comprises at least one metal ion selected from the group consisting of transition metal ions and post-transition metal ions. D includes at least one element selected from the group consisting of elements in groups IIIA and IVA of the periodic table. B contains at least one first alkali metal ion, B' comprises at least one first ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, Z contains at least one second alkali metal ion, Z' comprises at least one second ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, M contains at least one transition metal ion, A contains at least one chalcogen anion, A' contains at least one halogen anion, The aforementioned compound is a crystalline compound. [Claim 2] The compound according to claim 1, wherein L comprises Bi, Tl, Cu, or Hg. [Claim 3] The compound according to claim 1 or 2, wherein D comprises C, Si, Ge, Sn, Pb, or Al. [Claim 4] The compound according to claim 1 or 2, wherein B comprises Li, Na, K, Rb, or Cs. [Claim 5] The compound according to claim 4, wherein B comprises K, Rb, or Cs. [Claim 6] The compound according to claim 1 or 2, wherein B' comprises La, Mg, Ca, Sr, or Ba. [Claim 7] The compound according to claim 6, wherein B' comprises La, Ca, Sr, or Ba. [Claim 8] The compound according to claim 1 or 2, wherein Z comprises Li, Na, K, Rb, or Cs. [Claim 9] The compound according to claim 1 or 2, wherein Z' comprises Ca or Y. [Claim 10] M is the compound according to claim 1 or 2, comprising Cu or Fe. [Claim 11] A is the compound according to claim 1 or 2, comprising O, S, or Se. [Claim 12] A' is the compound according to claim 1 or 2, comprising F, Cl, Br, or I. [Claim 13] The compound according to claim 1 or 2, wherein the compound satisfies the equation: x*r + t*q = s. [Claim 14] The aforementioned compound is given by formula (Ia): L ｎ D ｍ (B ｘ B’ １－ｘ ) ｒ (Z ｔ Z’ １－ｔ ) ｑ M ｐ A ｙ A’ ｓ A” ｕ (Ia) The compound according to claim 1 or 2, wherein A'' is a halogen anion and is different from A', and u is a number from 0 to 20. [Claim 15] The compound according to claim 14, wherein the compound satisfies the equation: x * r = s. [Claim 16] The compound according to claim 15, further satisfying the equation: t*q = u. [Claim 17] The compound according to claim 1 or 2, wherein B' is a metal ion having a first atomic number, and Z' is a metal ion having a second atomic number, the second atomic number being smaller than the first atomic number. [Claim 18] The compound according to claim 1 or 2, wherein the compound is a superconductor at a temperature of at least 150 K. [Claim 19] The compound according to claim 18, wherein the compound is a superconductor at a temperature of at least 200 K. [Claim 20] The compound according to claim 1 or 2, wherein the compound has a tetragonal or orthorhombic crystal structure. [Claim 21] It is a compound, The compound is a crystalline metal oxide comprising at least one transition metal ion, at least one alkaline earth metal ion or at least one rare earth metal ion, and at least one chalcogen anion, wherein 10% to 100% of the at least one alkaline earth metal ion or at least one rare earth metal ion is replaced by the alkali metal ion, and 10% to 100% of the at least one chalcogen anion is replaced by a halogen anion. [Claim 22] The crystalline metal oxide before modification is Bi ２ Sr ２ CaCu ２ O ｙ , Bi ２ Sr ２ Ca ２ Cu ３ O ｙ , or YBa ２ Cu ３ O ｙ The compound according to claim 21. [Claim 23] The compound according to claim 21 or 22, wherein the alkali metal ion comprises Li, Na, K, Rb, or Cs. [Claim 24] The compound according to claim 21 or 22, wherein 50% to 100% of the at least one alkaline earth metal ion or at least one rare earth metal ion is replaced by the alkali metal ion. [Claim 25] The compound according to claim 21 or 22, wherein the halogen anion comprises F, Cl, Br, or I. [Claim 26] The compound according to claim 21 or 22, wherein at least one vertex chalcogen anion is replaced by the halogen anion. [Claim 27] A composition comprising the compound described in claim 1 or 22. [Claim 28] It is a method, A step of mixing at least one metal oxide with at least a first salt and a second salt, wherein the at least one metal oxide comprises at least one transition or post-transition metal cation, the first salt is an alkali metal halogen salt containing an alkali metal cation and a halogen anion for forming the mixture, and the second salt comprises an alkaline earth or rare earth metal cation, wherein the atomic ratio between the alkali metal cation and the alkaline earth or rare earth metal cation is at least 1:

1. The steps include: sintering the mixture at a high temperature to form a crystalline compound containing the alkali metal cation and the halogen anion; Methods that include... [Claim 29] The aforementioned metal oxide is CuO, Y ２ O ３ , or Bi ２ O ３ The method according to claim 28. [Claim 30] The method according to claim 28 or 29, wherein the second salt comprises an alkaline earth metal cation and at least one carbonate anion. [Claim 31] The second salt is CaCO2. ３ BaCO ３ , or SrCO ３ The method according to claim 30, including the method described in claim 30. [Claim 32] The method according to claim 28, wherein the step of sintering the mixture comprises sintering the mixture in an inert atmosphere. [Claim 33] The crystalline compound comprises a modified yttrium barium copper oxide (YBCO) material. The method according to claim 28, wherein the high temperature is 700°C to 850°C. [Claim 34] The crystalline compound comprises a modified bismuth strontium calcium copper oxide (BSCCO) material. The method according to claim 28, wherein the high temperature is 690°C to 820°C. [Claim 35] The method according to claim 34, wherein the high temperature is 690°C to 750°C. [Claim 36] The method according to claim 28, wherein the high temperature is less than 850°C. [Claim 37] The method according to claim 28, wherein the step of sintering the mixture comprises sintering the mixture for 24 to 96 hours. [Claim 38] The steps include grinding the crystalline compound, The steps include: resintering the pulverized crystalline compound, The method according to claim 28, including the method described in claim 28. [Claim 39] The method according to claim 28, comprising the step of melting and recrystallizing the crystalline compound using a micro-pulling-down (μ-PD) process in an inert atmosphere to obtain crystalline fibers. [Claim 40] The method according to claim 39, wherein the crystalline fiber comprises at least 90 volume percent of a Bi2212 compound, a Bi2201 compound, or both a Bi2212 compound and a Bi2201 compound. [Claim 41] The method according to claim 39, wherein the purity of the superconducting composition in the crystalline fiber is at least 90%. [Claim 42] The method according to claim 39, further comprising the step of applying a temperature gradient of 10°C / mm to 100°C / mm in the growth direction during the μ-PD process. [Claim 43] The method according to claim 39, further comprising the step of applying an axial temperature gradient of 100°C / mm to 300°C / mm during the μ-PD process. [Claim 44] A crystalline compound formed by the method described in claim 28 or 29. [Claim 45] An apparatus comprising the compound described in claim 1 or 2, A device that is superconducting at a temperature of at least 200K. [Claim 46] The apparatus according to claim 45, wherein the apparatus is a cable, a magnet, a levitation device, a superconducting quantum interference element, a bolometer, a thin-film element, a motor, a generator, a current limiter, a superconducting magnetic energy storage device, a quantum computer, a communication device, a high-speed single-flux quantum device, a magnetic confinement fusion reactor, a beam steering and confinement magnet, an RF filter, a microwave filter, or a particle detector. [Claim 47] A fault current limiting device, An electrical conducting element comprising a superconducting material having a superconducting state below a critical current and a normal conducting state above a critical current, the superconducting material comprising a crystalline compound containing at least one alkali metal ion, at least one first ion selected from the group consisting of alkaline earth metal ions and rare earth metal ions, and at least one halogen ion, A pair of electrical contacts are provided, located at the opposite end of the electrical conductive element and configured to connect the electrical conductive element to an electrical circuit. A heat sink that is in thermal communication with the superconducting material of the electrical conductive element, A fault current limiting device equipped with the above. [Claim 48] The apparatus according to claim 47, wherein the superconducting material is superconducting at room temperature for currents below the critical current. [Claim 49] The apparatus according to claim 47, wherein the critical current is 1 ampere or more at room temperature. [Claim 50] The apparatus according to claim 49, wherein the critical current threshold is in the range of 1 ampere to 1 kiloampere at room temperature. [Claim 51] The apparatus according to claim 47, further comprising a resistor electrically connected in parallel with the electrical conductive element. [Claim 52] The apparatus according to claim 47, wherein the electrical conductive element includes a conductive material that comes into contact with the superconducting material. [Claim 53] The apparatus according to claim 52, wherein the conductive material is copper. [Claim 54] Further comprising one or more additional electrical conductive elements, The pair of electrical contacts are located at the opposite ends of each of the one or more additional electrical conductive elements. The apparatus according to claim 47. [Claim 55] The apparatus according to claim 47, wherein the heat sink includes sapphire. [Claim 56] The apparatus according to claim 47, wherein the critical temperature of the superconducting material is 200 K or higher. [Claim 57] The apparatus according to claim 56, wherein the critical temperature is 250 K or higher. [Claim 58] The apparatus according to claim 57, wherein the critical temperature is 300 K or higher. [Claim 59] The apparatus according to claim 47, wherein the fault current limiting device is a resistive fault current limiting device. [Claim 60] The apparatus according to claim 47, wherein the fault current limiting device is an inductive fault current limiting device. [Claim 61] The apparatus according to claim 47, further comprising a cooling system that is in thermal communication with the superconducting material and configured to maintain the superconducting material below a critical temperature during operation of the apparatus. [Claim 62] The apparatus according to claim 61, wherein the cooling system is a water cooling system.

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