Patterned two-dimensional electron gas topology pitch line semimetal and design method thereof

Abstract

The invention discloses a patterned two-dimensional electron gas topology pitch line semimetal and a design method thereof, and the design method comprises the steps: carrying out the symmetry analysis of 17 types of two-dimensional wallpaper groups, and dividing the 17 types of wallpaper groups into two-dimensional dot type / non-dot type groups according to the symmetry analysis result, namely whether non-dot type operation exists or not; lattice structure design is carried out on the non-point group, the position of each lattice point is determined, and an external periodic adsorption layer structure is obtained; filling the patterned two-dimensional electron gas model according to the designed adsorption layer structure to obtain a patterned two-dimensional electron gas superlattice structure; the patterning two-dimensional electron gas superlattice topology nodal line semimetal energy band structure is researched by adopting multiple methods, and the method comprises three research methods of symmetry analysis, numerical calculation and analytical processing. According to the invention, a new possibility is provided for the design of the topological quantum device based on the topological Dirac nodal line semimetal, and the method has extremely high scientific research value and application potential.

Description

Technical Field

[0001] The present invention relates to the technical field of nanomaterials, and more specifically to a patterned two-dimensional electron gas topological node line semimetal and a design method thereof. Background Art

[0002] In the past few decades, topological materials have become a hot topic in condensed matter physics research, among which topological semimetals are an important member, including Dirac, Weyl and nodal line semimetals. Unlike Dirac and Weyl semimetals with discrete intersections, these intersections in nodal line semimetals form continuous lines or closed loops near the Fermi level. According to the degree of degeneracy, nodal line semimetals can be further divided into Dirac nodal line semimetals and Weyl nodal line semimetals. Since the behavior of low-energy quasiparticles in nodal line materials is different from that of traditional Schrödinger-type fermions, it has many novel properties, such as abnormal chirality, nearly flat tympanic surface states, unique Landau energy levels, and abnormal electromagnetic and transport responses, and is expected to realize new states of matter such as high-temperature superconductivity, laying the foundation for the realization of applications based on topological quantum devices.

[0003] On the one hand, in device design, compared with three-dimensional materials, two-dimensional materials have a smoother interface, which can effectively avoid device performance problems caused by interface disorder. In addition, its thickness is only a few atomic layers, and its properties can be controlled over a large range, which will bring breakthroughs in the application of devices based on topological nodal line semimetals. On the other hand, existing topological nodal line semimetal materials are all based on inherent crystallographic symmetry protection, which places high demands on the materials, especially when the spin-orbit coupling in the material cannot be ignored, additional symmetry protection is also required. And even if the material is selected, it is easy to bring some problems, such as specific crystal plane restrictions and unstable configurations. Therefore, it is still difficult to find naturally occurring two-dimensional topological nodal line semimetal materials.

[0004] Compared with point-symmetry operations, non-point-symmetry operations are more likely to produce stable intersections because non-point symmetry can protect the intersections from the effects of spin-orbit coupling in the material itself, such as funnel-shaped dispersion, node chains, and Insulator. In recent years, in addition to relying on the inherent symmetry of the material itself, the use of external means to control the symmetry of the system has also been widely studied in theory and experiment. Patterned two-dimensional electron gas is a very effective method. With this method, any desired topological state can be designed without being constrained by the material. Therefore, combining the patterned two-dimensional electron gas method with non-point symmetry, it is expected to design a stable topological semimetal material. Summary of the invention

[0005] The present invention is to solve the problem that three-dimensional materials cannot avoid the device performance caused by interface disorder in device design, and the existing topological nodal line semimetal materials are based on inherent crystallographic symmetry protection, which has high requirements on materials, especially when the spin-orbit coupling in the material cannot be ignored, and additional symmetry protection is required. Even if the material is selected, it is easy to bring some problems, such as specific crystal plane restrictions and unstable configurations. At present, it is still difficult to find naturally occurring two-dimensional topological nodal line semimetal materials. A patterned two-dimensional electron gas topological nodal line semimetal and a design method thereof are provided. The adsorption layer of the patterned two-dimensional electron gas topological Dirac nodal line semimetal provided by the present invention and the two-dimensional electron gas single crystal substrate present an obvious two-dimensional periodic non-point symmetric structure.

[0006] In order to achieve the above-mentioned object, the present invention provides a patterned two-dimensional electron gas topological nodal line semimetal, characterized in that it is composed of an adsorption layer adsorbed on a patterned two-dimensional electron gas surface (15); the patterned two-dimensional electron gas single crystal substrate is a copper / gold (111) surface (15), and the adsorption layer is a periodic single atomic layer (14).

[0007] In a preferred embodiment, the periodic single atomic layer (14) is made of bismuth atoms (14).

[0008] In a preferred embodiment, the periodic adsorption layer (14) has a non-point symmetrical structure.

[0009] In a preferred embodiment, the degenerate points (11, 12, 13) of the patterned two-dimensional electron gas topological semimetal are protected by non-point symmetry.

[0010] On the other hand, the present invention also provides a design method for the above-mentioned patterned two-dimensional electron gas topological node line semimetal, comprising the following steps:

[0011] Step 1, perform symmetry analysis on 17 two-dimensional wallpaper groups in Wikipedia, select two-dimensional wallpaper groups containing non-point operations according to the symmetry analysis results and divide them into two-dimensional non-point groups;

[0012] Step 2, check the three-dimensional layer group table and the three-dimensional space group table, find the three-dimensional space groups corresponding to the two-dimensional non-point group one by one according to the symmetry operation of the two-dimensional non-point group in step 1, and obtain the space group number of each three-dimensional space group, and then use the material calculation software Materials Studio to construct a lattice structure (1-3) according to the found three-dimensional space group to obtain an external periodic adsorption layer structure; the lattice structure (1-3) includes a lattice vector (5) and a lattice point position (4);

[0013] Step 3, filling the patterned two-dimensional electron gas model according to the adsorption layer structure designed in step 2, and theoretically obtaining a patterned two-dimensional electron gas superlattice structure;

[0014] Step 4: preparing materials for the patterned two-dimensional electron gas superlattice structure described in step 3 to obtain a patterned two-dimensional electron gas topological semimetal.

[0015] Under the preferred embodiment, the construction of the lattice structure (1-3) described in step 2 includes the following steps: inputting the space group number and lattice constant of each of the three-dimensional non-point space groups one by one, and then arbitrarily adding a lattice point position, the lattice will automatically fill in all other lattice point positions according to the established three-dimensional space group symmetry to obtain an external periodic adsorption layer structure (1-3).

[0016] In a preferred embodiment, the material preparation method of the patterned two-dimensional electron gas superlattice structure preparation method described in step 4 is one of molecular adsorption, atomic adsorption, quantum well etching, atomic force microscope etching and "top-down" etching.

[0017] In a preferred embodiment, the method for preparing the material of the patterned two-dimensional electron gas superlattice structure preparation method in step 4 is atomic adsorption, and the atomic adsorption comprises the following steps:

[0018] a1. Under vacuum conditions, the (111) surface of the copper / gold single crystal substrate (15) is subjected to argon ion sputtering for 3 to 5 times, with a sputtering time of 15 to 20 minutes and a voltage of 800 to 1000 eV;

[0019] a2. heating the (111) surface of the copper / gold single crystal substrate (15) at a temperature of 780 to 850 K for a time of 25 to 35 min to obtain a clean and flat crystal surface;

[0020] a3. At room temperature, bismuth atoms (14) are evaporated and deposited onto the clean and flat crystal surface obtained in step a2 to allow the bismuth atoms (14) to fully move on the surface, thereby obtaining a sample;

[0021] a4. Heat the sample obtained in step a3 at a temperature of 500-600 K for 100-150 min to obtain a patterned two-dimensional electron gas topological node line semimetal (i.e., a bismuth single atomic layer 14 covering the copper / gold surface 15).

[0022] In the preferred embodiment, the spraying time in step a1 is 20 min, and the vacuum condition is a vacuum degree higher than 2×10 - 10mbar, the purity of the copper / gold single crystal substrate (15) is 99.999%; the heating time in step a2 is 30 minutes, and the heating temperature is 800K; the room temperature in step a3 is 22-27°C, and the evaporation deposition is to evaporate the bismuth atoms (14) onto the clean and flat crystal surface obtained in step a2 using a Knudsen container through a thermal resistance evaporation source; the temperature in step a4 is 550K, and the heating time is 2 hours.

[0023] In the preferred embodiment, the external periodic potential type in the patterned two-dimensional electron gas model adopts Muffin-tin potential, and the potential energy is a constant value U within the range of Muffin-tin circle (4). 0 (>0), beyond this range the potential energy is 0.

[0024] In a more detailed scheme, the present invention provides a design method for a patterned two-dimensional electron gas topological node line semimetal, comprising the following steps:

[0025] Step 1: Perform symmetry analysis on all 17 two-dimensional wallpaper groups in Wikipedia, and divide all wallpaper groups into two-dimensional point / non-point groups according to the results of the symmetry analysis, i.e., whether they contain non-point operations;

[0026] Step 2, designing a lattice structure for the non-point group described in step 1, and determining the position of each lattice point (4), wherein the determination method is: according to the corresponding symmetry operation in the non-point group, the corresponding three-dimensional space group is found one by one by checking the layer group and space group table, and then the material calculation software Materials Studio is used to construct a lattice structure (1-3) according to the found space group, including a lattice vector (5) and a lattice point position (4), thereby obtaining an external periodic adsorption layer structure;

[0027] Step 3, filling the patterned two-dimensional electron gas model according to the adsorption layer structure designed in step 2, and theoretically obtaining a patterned two-dimensional electron gas superlattice structure;

[0028] Step 4: Use a variety of methods to study the band structure of the patterned two-dimensional electron gas superlattice topological semimetal, including symmetry analysis, numerical calculation, and analytical processing. Obtain degeneracy information by symmetry analysis of a small group of high symmetry points / lines (7) in the Brillouin zone (6); numerically calculate the eigenvalues ​​of the Hamiltonian of the patterned two-dimensional electron gas model and draw the band diagram; use degenerate perturbation theory to analytically process the dispersion relations near the topological degenerate points / lines (11, 12, 13);

[0029] Step 4 is the theoretical calculation part. The results obtained by the three research methods can all confirm that the constructed patterned two-dimensional electron gas superlattice is indeed a topological nodal line semimetal. Theory first, then experiment, and the subsequent step 5 is experimental preparation.

[0030] Step 5, preparing a patterned two-dimensional electron gas topological nodal line semimetal: preparing materials for the patterned two-dimensional electron gas superlattice described in step 3, using atomic adsorption as the preparation method, wherein the two-dimensional electron gas single crystal substrate is a copper / gold (111) surface (15), and the adsorption layer is a bismuth atom (14).

[0031] In some embodiments of the present invention, the patterned two-dimensional electron gas topological nodal line semimetal is composed of a periodic single atomic layer (14) adsorbed on a two-dimensional electron gas material surface (15).

[0032] In some embodiments of the present invention, the periodic adsorption layer (14) has a non-point symmetric structure.

[0033] In some embodiments of the present invention, the degenerate points (11, 12, 13) of the topological semimetal are protected by non-point symmetry.

[0034] In some embodiments of the present invention, the external periodic potential type in the patterned two-dimensional electron gas model adopts Muffin-tin potential, and the potential energy is constant within the range of the Muffin-tin circle (4), and the potential energy is 0 outside this range.

[0035] In some embodiments of the present invention, there are multiple methods for preparing the patterned two-dimensional electron gas superlattice material, including molecular / atomic adsorption, quantum well etching, atomic force microscope etching and "top-down" etching, and the periodic structure can be characterized by a scanning tunneling microscope.

[0036] The beneficial effects of the present invention are:

[0037] The present invention establishes a general principle for designing non-point symmetry protected topological Dirac nodal line semimetals in nano-patterned two-dimensional electron gas, effectively utilizes external periodic potential to regulate the symmetry and band structure of the system, enriches the two-dimensional topological semimetal family, and provides new possibilities for the design of topological quantum devices based on topological Dirac nodal line semimetals. At the same time, this design idea can be easily extended to other self-assembled surface systems, and has extremely high scientific research value and application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagrams of five two-dimensional non-point groups of the present invention, namely p1g1, p2mg, p2gg, c1m1;

[0039] Figure 2 It is a design flow chart of a topological semimetal with non-point symmetric protection under the patterned two-dimensional electron gas model of the present invention;

[0040] Figure 3 (a)-3(c) are schematic diagrams of three two-dimensional lattice structures with non-point symmetry constructed by the present invention; Figure 3 (d) Yes Figure 3 (a) and Figure 3 (b) the Brillouin zone of the lattice structure, Figure 3 (e) Yes Figure 3 (c) a Brillouin zone of the lattice structure;

[0041] Figure 4-Figure 6 is the two-dimensional / three-dimensional energy band diagram of the patterned two-dimensional electron gas superlattice structure calculated by the present invention, corresponding to Figure 3 (a)-3(c) Schematic diagram of lattice structure;

[0042] Figure 7 and Figure 8 is a diagram of the atomic structure model of the patterned two-dimensional electron gas topological semi-metal superlattice on the copper / gold (111) surface of the present invention, corresponding to Figure 3 (a) and Figure 3 (b) Schematic diagram of the lattice structure.

[0043] In the figure, 1. Two-dimensional lattice structure with wallpaper group p2mg symmetry; 2. Two-dimensional lattice structure with wallpaper group p2gg symmetry; 3. Two-dimensional lattice structure with wallpaper group p4mg symmetry; 4. Muffin-tin circle; 5. Lattice constant; 6. Brillouin zone; 7. High symmetry point; 8-10. Four energy bands with the lowest energy; 11-13. Dirac nodal lines; 14. Periodic bismuth single atom adsorption layer; 15. (111) surface of two-dimensional electron gas material copper / gold; 16. Primitive cell. DETAILED DESCRIPTION

[0044] The present invention provides a patterned two-dimensional electron gas topological nodal line semimetal and a design method thereof. It includes symmetry analysis of all 17 two-dimensional wallpaper groups, and dividing all wallpaper groups into two-dimensional point / non-point groups according to the result of the symmetry analysis, i.e., whether they contain non-point operations; designing the lattice structure of the non-point group, determining the position of each lattice point, and obtaining an external periodic adsorption layer structure; filling the patterned two-dimensional electron gas model according to the designed adsorption layer structure to obtain a patterned two-dimensional electron gas superlattice structure; and using a variety of methods to study the band structure of the patterned two-dimensional electron gas superlattice topological nodal line semimetal, including three research methods of symmetry analysis, numerical calculation, and analytical processing. This will be further explained below in conjunction with the embodiments and drawings.

[0045] A design method for a patterned two-dimensional electron gas topological nodal line semimetal comprises the following steps:

[0046] Step 1: Divide the two-dimensional point / non-point groups:

[0047] Symmetry analysis was performed on all 17 2D wallpaper groups in Wikipedia (https: / / en.wikipedia.org / wiki / Wallpaper_group) (Table 1), and the characteristics of each group were used to find out whether it contained non-point symmetry, namely, sliding reflection. After analysis, there are 5 2D wallpaper groups containing non-point operations, which are ranked from low to high in terms of symmetry, namely, p1g1, p2mg, p2gg, c1m1, and p4gm (e.g. Figure 1 ). The four letters or symbols represent the following meanings: the first letter p / c represents the unit cell, the second number n represents the highest-order rotation axis, the third letter g / m represents the slip plane / mirror plane perpendicular to a certain translation axis, the fourth letter g / m represents the slip plane / mirror plane parallel to the translation axis or sandwiched by a 180° / n angle, and 1 represents neither. Specifically, the wallpaper group p2mg contains a slip axis in the y direction ( Figure 1 The wallpaper groups p2gg and p4gm both contain sliding axes in the x and y directions; although the wallpaper group p1g1 also contains sliding axes in the x direction, it does not contain rotation and mirror reflection. In a broad sense, it can be regarded as a one-dimensional system, so it is not considered; the sliding reflection operation in the x direction contained in the wallpaper group c1m1 can be obtained by combining two parallel mirror operations, which is also not considered. Therefore, the 17 two-dimensional wallpaper groups are divided into 3 two-dimensional non-point groups (p2mg, p2gg and p4gm) and the remaining 14 two-dimensional point groups.

[0048] Table 1 17 types of two-dimensional wallpaper groups

[0049]

[0050] Step 2: Design the configuration of the additional adsorption layer:

[0051] Design the three-dimensional lattice structure for the three non-point groups (p2mg, p2gg and p4gm) divided in step 1, and determine the position of each lattice point. This requires the use of the three-dimensional layer group as a bridge, because in mathematics, the layer group is a three-dimensional extension of the wallpaper group. It is a space group with a two-dimensional lattice. Compared with the wallpaper group, it only has mirror reflection in the third direction (z direction). The determination method is: check the three-dimensional layer group table (https: / / en.wikipedia.org / wiki / Layer_group) (Table 2) and the three-dimensional space group table (https: / / en.wikipedia.org / wiki / Space_group) (Table 3) on Wikipedia to find the three-dimensional space groups corresponding to the three non-point groups in step 1 one by one. After analysis, the wallpaper group p2mg (with mirror reflection perpendicular to the y-axis and sliding reflection perpendicular to the x-axis) corresponds to the layer group pmma and the space group Pmma (No. 51, with mirror planes perpendicular to the x- and y-axes and sliding reflection perpendicular to the z-axis, the symbol m represents the mirror plane, and a / b represents the sliding mirror plane); the wallpaper group p2gg (with sliding reflection perpendicular to the x- and y-axes, the symbol g represents the sliding mirror plane) corresponds to the layer group pbam and the space group Pbam (No. 55, with sliding reflections perpendicular to the x and y axes and a mirror plane perpendicular to the z axis); wallpaper group p4gm (with sliding reflections perpendicular to the x / y axis and a mirror plane at 45° to the x / y direction) corresponds to layer group p4 / mbm and space group P4 / mbm (No. 127, with a mirror plane perpendicular to the z axis, a sliding reflection perpendicular to the x / y axis and a mirror plane in a 45° direction, the symbol 4 / m indicates that there is both a four-degree axis and a mirror plane perpendicular to the axis in the z direction). Then, the materials calculation software Materials Studio is used according to the software learning tutorial ("CASTEP / Materials Studio Advanced Course in Computational Materials Science", Li Mingxian, June 2014) to build a lattice structure based on the three space groups found above, including lattice vector 5 and lattice point position 4. The specific operation process is as follows: first, enter the space group number and lattice constant to construct the lattice; then arbitrarily add an atom (lattice point) position, at this time the lattice will automatically fill in all other atomic positions according to the established space group symmetry, that is, obtain three additional periodic adsorption layer structures 1-3, such as Figure 3 (a)-3(c) are schematic diagrams of three types of two-dimensional lattice structures with non-point symmetry constructed by the present invention.

[0052] Table 2 Three-dimensional layer group table

[0053]

[0054]

[0055] Table 3 Three-dimensional space group table

[0056]

[0057]

[0058]

[0059] Step 3: Fill the patterned two-dimensional electron gas model:

[0060] The patterned two-dimensional electron gas model is filled according to the three adsorption layer structures 1-3 designed in step 2, and a patterned two-dimensional electron gas superlattice structure is theoretically obtained. The specific filling method refers to the Hamiltonian of the patterned two-dimensional electron gas model in the literature (N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Fort Worth, TX, 1976)):

[0061]

[0062] Among them, the first part on the right side of the equal sign is the kinetic energy term, and the second part is the pattern potential energy term, m * is the effective mass of the electron, G is the reciprocal lattice vector, k is the wave vector, a + and a are the generation and annihilation operators respectively, V(G) is the Fourier component of the periodic potential, and the specific expression is:

[0063]

[0064] Among them, X i is the center position of the i-th Muffin-tin circle 4 in the primitive cell, d is the radius of the Muffin-tin circle 4, A is the area of ​​the primitive cell 16, U 0 is the potential energy value of the patterned Muffin-tin circle, J 1 is a first-order Bessel function, and the sum i covers all Muffin-tin circles. Substitute the parameters of the three adsorption layer structures in step 2 into the above Hamiltonian to fill in and obtain the corresponding Hamiltonian matrix.

[0065] Here, the Hamiltonian matrix is ​​in the form of the Hamiltonian matrix corresponding to the patterned two-dimensional electron gas superlattice model. The model needs to be written as a Hamiltonian to solve the subsequent electron energy.

[0066] Step 4, calculating the energy band of the patterned two-dimensional electron gas model;

[0067] A variety of methods are used to study the band structure of patterned two-dimensional electron gas superlattice topological semimetal, including symmetry analysis, numerical calculation, and analytical processing. First, the degeneracy information is obtained by symmetry analysis of the small group of high symmetry points / lines 7 (Tinkham, M. Group Theory and Quantum Mechanics 279–281 (Dover, 2003)). After analysis, for the p2mg adsorption layer structure 1, the energy along the path XM is four-degree degenerate; for the p2gg adsorption layer structure 2, the energy along the path XM and YM is four-degree degenerate; for the p4mg adsorption layer structure 3, the energy along the path XM is also four-degree degenerate. Then, Matlab software is used to refer to the learning tutorial (MATLAB Basic Tutorial Third Edition, Xue Shan, 2017) to numerically solve the eigenvalues ​​(energy values) of the Hamiltonian matrices of the three patterned two-dimensional electron gas models in step 3 and draw the band diagram. Finally, the k·p degenerate perturbation theory (refer to the textbook "Quantum Theory of Solids", C.Kittel, 1987, pages 186-190) is used to analytically solve the energy-momentum relationship near the node line 11-13 and determine the type of topological node line.

[0068] Step 5: Prepare the material of the patterned two-dimensional electron gas superlattice described in step 3. The preparation method uses atomic adsorption (reference MYTian et al., Nano Lett. 20, 2157 (2020)), wherein the two-dimensional electron gas substrate 15 uses the (111) surface of single crystal copper / gold, and the adsorption layer 14 uses bismuth atoms. The specific operation method is: first, in a vacuum environment (vacuum degree higher than 2×10 -10 The (111) surface of a copper / gold single crystal substrate 15 (purity 99.999%) is subjected to argon ion sputtering 3-5 times at 800-1000 eV (mbar), and each sputtering time is maintained at 20 minutes (800-1000 eV). The copper / gold substrate 15 is then heated and maintained at 800K for 30 minutes to obtain a clean and flat crystal surface, and the crystal surface is detected using a scanning tunneling microscope and an angle-resolved optical emission spectrometer. Thereafter, at room temperature, bismuth atoms 14 are evaporated and deposited onto the clean and flat copper / gold (111) surface 15 using a Knudsen container through a thermal resistance evaporation source, so that the bismuth atoms 14 can move fully on the surface. After the evaporation is completed, the sample is heated at 550K for 2 hours, then cooled and measured by a scanning tunneling microscope and an angle-resolved optical emission spectrometer, and finally a bismuth single atomic layer 14 (such as Figure 7-8 As shown, bismuth atoms 14 form a non-point symmetrical structure 1-2) on the copper / gold surface 15.

[0069] Furthermore, the periodic adsorption layer has a non-point symmetric structure.

[0070] Furthermore, the degenerate points / lines of the topological semimetal are protected by non-point symmetry.

[0071] Furthermore, the external periodic potential type in the patterned two-dimensional electron gas model adopts the Muffin-tin potential, and the potential energy U 0 It is a constant value, and the potential energy is 0 outside this range.

[0072] As a preferred embodiment of the present invention, the patterned two-dimensional electron gas periodic material structure can be characterized by a scanning tunneling microscope, that is, the designed structure and material can be confirmed by instrument observation.

[0073] The present invention proposes a patterned two-dimensional electron gas topological semimetal material and a design method thereof. A two-dimensional non-point symmetric adsorption layer structure is constructed through symmetry analysis, and then filled into the patterned two-dimensional electron gas model to obtain stable degenerate points / lines protected by non-point symmetry. Compared with the existing methods for discovering naturally existing topological semimetal materials, the present invention adopts an external symmetry processing method according to the distribution law of degenerate points and design requirements, and artificially transforms the symmetry of the base material by adsorbing a single atomic layer with an ideal structure, thereby greatly improving the ability to artificially construct exotic topological semimetals. Especially for scarce topological semimetal materials, symmetry processing is more flexible, which has great application potential for the study of novel physical states based on topological semimetals and the design and manufacture of topological quantum devices.

[0074] Example 1

[0075] The overall design flow chart of the present invention is as follows: Figure 2 A design method for a patterned two-dimensional electron gas topological node line semimetal, the specific steps are:

[0076] Step 1: Divide the two-dimensional point / non-point groups:

[0077] Symmetry analysis is performed on all 17 two-dimensional wallpaper groups. Based on the results of the symmetry analysis, wallpaper groups without non-point operations are divided into two-dimensional point groups, and wallpaper groups with non-point operations are divided into two-dimensional non-point groups.

[0078] The method of dividing wallpaper groups into point / non-point groups through symmetry analysis in step 1 is based on whether they contain non-point operations. After analysis, there are 5 wallpaper groups containing non-point operations - slip axes, which are p1g1, p2mg, p2gg, c1m1 and p4gm in descending order of symmetry. Among them, wallpaper group p2mg contains a slip axis in one direction; wallpaper groups p2gg and p4gm both contain slip axes in two directions perpendicular to each other; although wallpaper group p1g1 also contains a slip axis, it can be regarded as a one-dimensional system in a broad sense, so it is not considered; the slip axis operation contained in wallpaper group c1m1 can be obtained by combining two parallel mirror operations, which is also not considered. Therefore, the 17 two-dimensional wallpaper groups are divided into 3 non-point groups and 14 point groups in total.

[0079] Step 2: Design the additional adsorption layer configuration 1-3:

[0080] Design the three-dimensional lattice structure for the three non-point groups in step 1 and determine the position of each lattice point;

[0081] In step 2, determining the non-point three-dimensional lattice structure requires using the three-dimensional layer group as a bridge to find the one-to-one correspondence between the wallpaper group and the three-dimensional space group. After analysis, the wallpaper group p2mg corresponds to the layer group pmma and the space group Pmma (No. 51); the wallpaper group p2gg corresponds to the layer group pbam and the space group Pbam (No. 55); the wallpaper group p4gm corresponds to the layer group p4 / mbm and the space group P4 / mbm (No. 127). Then use the material calculation software Materials Studio to build a lattice structure based on the three space groups found, including the lattice vector 5 and the lattice position 4, so as to obtain three external periodic adsorption layer structures 1-3, such as Figure 3 (a)-3(c) shown.

[0082] Step 3: Fill the patterned two-dimensional electron gas model:

[0083] The patterned two-dimensional electron gas model is filled according to the three adsorption layer structures 1-3 designed in step 2, and a patterned two-dimensional electron gas superlattice structure is theoretically obtained;

[0084] The Hamiltonian of the patterned two-dimensional electron gas model is:

[0085]

[0086] Among them, m * is the effective mass of the electron, G is the reciprocal lattice vector, a + and a are the creation and annihilation operators respectively, V(G) is the Fourier component of the periodic potential, which can be expressed as:

[0087]

[0088] Among them, X i is the center position of the ith Muffin-tin circle 4 in the primitive cell, d is the radius of the Muffin-tin circle 4, and A is the area of ​​the primitive cell 16. Substitute the structural parameters of the adsorption layer in step 2 into the above Hamiltonian for filling.

[0089] Step 4: Calculate the energy band of the patterned two-dimensional electron gas superlattice:

[0090] A variety of methods are used to study the band structure of the patterned two-dimensional electron gas model, including symmetry analysis, numerical calculation, and analytical processing;

[0091] First, we obtain the degeneracy information by symmetry analysis of the small group of high symmetry points / lines 7. For the p2mg adsorption layer structure 1, the energy along the XM path is four-degree degenerate; for the p2gg adsorption layer structure 2, the energy along the XM and YM paths is four-degree degenerate; for the p4mg adsorption layer structure 3, the energy along the XM path is also four-degree degenerate. Then, we numerically solve the eigenvalues ​​of the Hamiltonian of the patterned two-dimensional electron gas model in step 3 and draw the energy band diagram. The results are shown in Figure 2. Figure 4-6 As shown, the four lowest energy bands 8-10 of each adsorption layer structure have Dirac nodal lines 11-13. Finally, the dispersion relation near the nodal lines 11-13 is analytically solved using degenerate perturbation theory, and a linear energy-momentum relation is obtained, which further proves that a non-point symmetry-protected topological Dirac nodal line semimetal is designed on a two-dimensional electron gas using an external periodic potential.

[0092] Step 5: Preparation of patterned two-dimensional electron gas topological Dirac node line semimetal:

[0093] There are many methods for preparing the topological Dirac nodal line semimetal described in step 4, including molecular / atomic adsorption, quantum well etching, atomic force microscope etching and "top-down" etching. As a preferred method of the present invention, atomic adsorption is selected as the preparation method, wherein the two-dimensional electron gas single crystal substrate 15 is selected from the (111) surface of copper / gold, and the adsorption layer 14 is selected from bismuth atoms.

[0094] First, in a vacuum environment (vacuum degree higher than 2×10 -10The (111) surface of a copper / gold single crystal substrate 15 (purity 99.999%) is subjected to argon ion sputtering 3-5 times at 800-1000 eV (mbar), and each sputtering time is maintained at 20 minutes (800-1000 eV). The copper / gold substrate 15 is then heated and maintained at 800 K for 30 minutes to obtain a clean and flat crystal surface, and the crystal surface is detected using a scanning tunneling microscope and an angle-resolved optical emission spectrometer. Thereafter, bismuth atoms 14 are evaporated and deposited onto the clean and flat copper / gold (111) surface 15 at room temperature using a thermal resistance evaporation source, so that the bismuth atoms 14 can move fully on the surface. After the evaporation is completed, the sample is heated at 550 K for 2 hours, then cooled and measured by a scanning tunneling microscope and an angle-resolved optical emission spectrometer, and finally a bismuth single atomic layer 14 (such as Figure 7-8 As shown, bismuth atoms 14 form a non-point symmetrical structure 1-2) on the copper / gold surface 15.

[0095] The present invention establishes a general principle for designing non-point symmetry protected topological Dirac nodal line semimetals in nano-patterned two-dimensional electron gas, effectively utilizes an external periodic potential to regulate the symmetry and band structure of the system, enriches the family of two-dimensional topological Dirac nodal line semimetals, and provides new possibilities for the design of topological quantum devices based on topological Dirac nodal line semimetals. At the same time, this design idea can be easily extended to other self-assembled surface systems, and has extremely high scientific research value and application potential.

[0096] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A patterned two-dimensional electron gas topological nodal line semimetal, It is characterized in that It is composed of an adsorption layer adsorbed on a two-dimensional electron gas surface (15); the patterned two-dimensional electron gas single crystal substrate is a copper / gold (111) surface (15), and the adsorption layer is a periodic single atomic layer (14).

2. The patterned two-dimensional electron gas topological nodal line semimetal according to claim 1, It is characterized in that The periodic single atomic layer (14) is made of bismuth atoms (14).

3. The patterned two-dimensional electron gas topological node line semimetal according to claim 1 or 2, It is characterized in that The periodic adsorption layer (14) has a non-point symmetric structure.

4. The patterned two-dimensional electron gas topological node line semimetal according to claim 1 or 2, It is characterized in that The degenerate points (11, 12, 13) of the patterned two-dimensional electron gas topological semimetal are protected by non-point symmetry.

5. A method for designing a patterned two-dimensional electron gas topological nodal line semimetal according to any one of claims 1 to 4, It is characterized in that The steps include: Step 1, perform symmetry analysis on 17 two-dimensional wallpaper groups in Wikipedia, select two-dimensional wallpaper groups containing non-point operations according to the symmetry analysis results and divide them into two-dimensional non-point groups; Step 2, check the three-dimensional layer group table and the three-dimensional space group table, find the three-dimensional space groups corresponding to the two-dimensional non-point group one by one according to the symmetry operation of the two-dimensional non-point group in step 1, and obtain the space group number of each three-dimensional space group, and then use the material calculation software Materials Studio to construct a lattice structure (1-3) according to the found three-dimensional space group to obtain an external periodic adsorption layer structure; the lattice structure (1-3) includes a lattice vector (5) and a lattice point position (4); Step 3, filling the patterned two-dimensional electron gas model according to the adsorption layer structure designed in step 2, and theoretically obtaining a patterned two-dimensional electron gas superlattice structure; Step 4: preparing materials for the patterned two-dimensional electron gas superlattice structure described in step 3 to obtain a patterned two-dimensional electron gas topological semimetal.

6. The design method of the patterned two-dimensional electron gas topological nodal line semimetal according to claim 5, It is characterized in that The construction of the lattice structure (1-3) described in step 2 includes the following steps: inputting the space group number and lattice constant of each of the three-dimensional non-point space groups one by one, and then adding a lattice point position at random. The lattice will automatically fill in all other lattice point positions according to the established three-dimensional space group symmetry to obtain an external periodic adsorption layer structure (1-3).

7. The design method of the patterned two-dimensional electron gas topological nodal line semimetal according to claim 5, It is characterized in that The preparation method of the material of the patterned two-dimensional electron gas superlattice structure preparation method described in step 4 is one of molecular adsorption, atomic adsorption, quantum well etching, atomic force microscope etching and "top-down" etching.

8. The design method of the patterned two-dimensional electron gas topological nodal line semimetal according to claim 7, It is characterized in that The method for preparing the patterned two-dimensional electron gas superlattice structure material in step 4 is atomic adsorption, and the atomic adsorption comprises the following steps: a1. Under vacuum conditions, the (111) surface of the copper / gold single crystal substrate (15) is subjected to argon ion sputtering for 3 to 5 times, with a sputtering time of 15 to 20 minutes and a voltage of 800 to 1000 eV; a2. heating the (111) surface of the copper / gold single crystal substrate (15) at a temperature of 780 to 850 K for a time of 25 to 35 min to obtain a clean and flat crystal surface; a3. At room temperature, bismuth atoms (14) are evaporated and deposited onto the clean and flat crystal surface obtained in step a2 to allow the bismuth atoms (14) to fully move on the surface, thereby obtaining a sample; a4. Heat the sample obtained in step a3 at a temperature of 500-600 K for 100-150 min to obtain a patterned two-dimensional electron gas topological node line semimetal.

9. The design method of the patterned two-dimensional electron gas topological nodal line semimetal according to claim 8, It is characterized in that The spraying time in step a1 is 20 min, and the vacuum condition is a vacuum degree higher than 2×10 -10 mbar, the purity of the copper / gold single crystal substrate (15) is 99.999%; the heating time in step a2 is 30 minutes, and the heating temperature is 800K; the room temperature in step a3 is 22-27°C, and the evaporation deposition is to evaporate the bismuth atoms (14) onto the clean and flat crystal surface obtained in step a2 using a Knudsen container through a thermal resistance evaporation source; the temperature in step a4 is 550K, and the heating time is 2 hours.

10. The design method of the patterned two-dimensional electron gas topological nodal line semimetal according to claim 5, It is characterized in that The external periodic potential type in the patterned two-dimensional electron gas model adopts the Muffin-tin potential, and the potential energy is a constant value U within the Muffin-tin circle (4). 0 (>0), beyond this range the potential energy is 0.

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