Quantum apparatus and method for manufacturing a quantum apparatus

Abstract

The present invention provides a quantum device and a method for manufacturing the same that enable the injection of Cooper pairs into the edges of a two-dimensional topological insulator without the use of heterointerfaces, and the control of the Fermi level at the edges of the two-dimensional topological insulator. [Solution] The quantum device comprises a monolayer 4 of tungsten ditelluride having a 1T' type crystal structure, a first electrode 6a that provides a first potential to a first portion of the monolayer that is a part of the monolayer and separated from the outer periphery of the monolayer, and a second electrode 6b that provides a second potential to a second portion of the monolayer that is a part of the monolayer and includes a certain range of the outer periphery of the monolayer. The first electrode is positioned so that Cooper pairs generated by the application of the first potential to the first portion can penetrate a third portion that is a part of the second portion and includes the certain range. The third portion is a region in which topological superconductivity occurs when Cooper pairs penetrate.

Description

[Technical Field]

[0001] This invention relates to a quantum device and a method for manufacturing a quantum device. [Background technology]

[0002] Majorana particles are unique particles that are themselves antiparticles. However, it has recently been proposed that quasiparticles with Majorana particle characteristics (hereinafter referred to as Majorana quasiparticles) can appear in solids. Following this proposal, research aimed at realizing Majorana quasiparticles is being actively conducted. The realization of Majorana quasiparticles is important not only for physics but also for the realization of quantum computers that are robust against disturbances (see, for example, Patent Document 1 and Non-Patent Document 1).

[0003] One device attracting attention for generating Majorana quasiparticles is a device (hereinafter referred to as a topological quantum device) that has a two-dimensional topological insulator (hereinafter referred to as 2DTI), also known as a quantum spin Hall insulator (see, for example, Non-Patent Document 2). Majorana quasiparticles appear by joining a superconductor to the edge of a two-dimensional topological insulator. Quantum operations based on Majorana quasiparticles (i.e., quantum gate operations) can be realized by a qubit having multiple topological devices (hereinafter referred to as a Majorana qubit) (see, for example, Non-Patent Document 2).

[0004] A single layer of tungsten ditelluride (hereinafter referred to as single-layer WTe2) is one of the few materials confirmed to be a two-dimensional topological insulator. Regarding single-layer WTe2, it has been reported that applying a voltage to the gate electrode on an insulating film in contact with the single-layer WTe2 induces superconductivity in the single-layer WTe2 (hereinafter referred to as field-induced superconductivity) (for example, Non-Patent Documents 3-6).

[0005] Apart from these reports, there are also reports concerning devices having a thin layer or single layer of tungsten ditelluride WTe2 and a gate electrode (see, for example, Patent Document 2 and Non-Patent Documents 7 and 8). There are also reports concerning devices having a superconductor and a gate electrode (see, for example, Patent Documents 3 and 4). The band structure of single layer WTe2 has been theoretically calculated (see, for example, Non-Patent Documents 7 and 8). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] U.S. Patent Application Publication No. 2022 / 0262856 [Patent Document 2] U.S. Patent Application Publication No. 2021 / 0159398 [Patent Document 3] Japanese Patent Publication No. 2003-67181 [Patent Document 4] Japanese Unexamined Patent Publication No. 64-24476 [Non-patent literature]

[0007] [Non-Patent Document 1] Osamu Machida, et al., "Observation of a Zero-Energy State Suggesting a Majorana Bound State," Journal of the Physical Society of Japan, 2020, Vol. 75, No. 9, pp. 570-572. [Non-Patent Document 2] B van Heck, et al., “Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator”, Phys. Scr. T164 (2015) 014007 [Non-Patent Document 3] Ebrahim Sajadi, et al., “Gate-induced superconductivity in a monolayer topological insulator”, Science, 2018, Vol. 362, p.922-925 [Non-Patent Document 4] Ebrahim Sajadi, et al., "Supplementary Materials for Gate-induced superconductivity in a monolayer topological insulator", [online], 25 October 2018, Science First Release, [Retrieved April 11, 2022], Internet<URL: https: / / www.science.org / doi / 10.1126 / science.aar4426> [Non-Patent Document 5] Valla Fatemi, et al., “Electrically tunable low-density superconductivity in a monolayer topological insulator”, Science, 2018, Vol. 362, p.926-929 [Non-Patent Document 6] Valla Fatemi, et al., "Supplementary Materials for Electrically tunable low-density superconductivity in a monolayer topological insulator", [online], 25 October 2018, Science First Release, [Retrieved April 11, 2022], Internet<https: / / www.science.org / doi / 10.1126 / science.aar4642> [Non-Patent Document 7] Xiaofeng Qian et al., “Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides”, [online], [searched on April 5, 2023], Internet <URL: https: / / arxiv.org / ftp / arxiv / papers / 1406 / 1406.2749.pdf>

Non-Patent Document 8

Summary of the Invention

Problems to be Solved by the Invention

[0008] The generation of Majorana quasiparticles is important for realizing a quantum computer that is resistant to disturbances.

[0009] When Cooper pairs penetrate into the edges of a two-dimensional topological insulator (i.e., a narrow region along the outer periphery), one-dimensional chiral p-wave superconductivity, which is a type of topological superconductivity, occurs. Majorana quasiparticles appear at both ends of the region where topological superconductivity occurs (for example, see Non-Patent Document 1).

[0010] A topological quantum device that causes Majorana quasiparticles to appear has, for example, a two-dimensional topological insulator, an S-wave superconductor that contacts a part of the outer periphery of the two-dimensional topological insulator, and ferromagnets arranged on both sides of the S-wave superconductor.

[0011] When a topological quantum device is cooled, Cooper pairs penetrate from an S-wave superconductor into the ends of a two-dimensional topological insulator (hereinafter referred to as 2DTI ends). Then, topological superconductivity occurs in the part where the Cooper pairs penetrate. This topological superconductivity is terminated by ferromagnetic materials arranged on both sides of the S-wave superconductor, and as a result, Majorana quasiparticle pairs appear.

[0012] Cooper pairs in the S-wave superconductor penetrate into the 2DTI ends through the interface between the two-dimensional topological insulator and the S-wave superconductor (hereinafter referred to as the heterointerface). However, conventional topological quantum devices have a problem that during their manufacturing process, an oxide film that suppresses the proximity effect is formed between the two-dimensional topological insulator and the S-wave superconductor. This is because, due to the structure of conventional topological quantum devices, at least one of the two-dimensional topological insulator and the S-wave superconductor is exposed to the atmosphere before forming the heterointerface.

[0013] Even if Cooper pairs can penetrate into the 2DTI ends, if the Fermi level of the penetrated part is not between the valence band and the conduction band, topological superconductivity suitable for the generation of Majorana quasiparticle pairs will not occur. However, when a foreign substance (e.g., an S-wave superconductor) contacts a two-dimensional topological insulator, the Fermi level may escape from between the valence band and the conduction band.

[0014] Therefore, the control of the Fermi level is important for the generation of Majorana quasiparticle pairs. However, conventional topological quantum devices also have a problem that they do not have a function to control the Fermi level.

[0015] Therefore, an object of the present invention is to solve these problems.

Means for Solving the Problems

[0016] In one embodiment, the quantum device comprises a monolayer of tungsten ditelluride having a 1T'-type crystal structure, a first electrode that applies a first potential to a first portion of the monolayer that is separated from the outer periphery of the monolayer, and a second electrode, different from the first electrode, that applies a second potential to a second portion of the monolayer that includes a certain range of the outer periphery. The first electrode is positioned so that Cooper pairs generated by the application of the first potential to the first portion can penetrate a third portion that is part of the second portion and includes the certain range. The third portion is the part in which topological superconductivity occurs when the Cooper pairs penetrate. [Effects of the Invention]

[0017] In one respect, the present invention enables the injection of Cooper pairs into the 2DTI end without the need for a heterointerface, and the control of the Fermi level at the 2DTI end. [Brief explanation of the drawing]

[0018] [Figure 1] Figure 1 is a plan view of an example of a quantum apparatus according to Embodiment 1. [Figure 2] Figure 2 is a cross-sectional view along the line II-II shown in Figure 1. [Figure 3] Figure 3 is a cross-sectional view along the line III-III shown in Figure 1. [Figure 4] Figure 4 is a plan view showing the portion of the single layer 4 related to the first to third electrodes. [Figure 5] Figure 5 is a plan view showing the relationship between the outer periphery of the first electrode 6a, the second electrode 6b, and the single layer 4. [Figure 6] Figure 6 is a plan view illustrating the physical properties of single layer 4. [Figure 7] Figure 7 is the energy band diagram at the single-layer end 26. [Figure 8] Figure 8 is an energy band diagram showing the electronic characteristics of single layer 4 when no electric field is applied. [Figure 9]Figure 9 is another energy band diagram showing the electronic characteristics of single layer 4 without an applied electric field. [Figure 10] Figure 10 is an energy band diagram showing the electronic characteristics of a single layer 4 to which a weak electric field has been applied. [Figure 11] Figure 11 is another energy band diagram showing the electronic properties of a single layer 4 to which a weak electric field has been applied. [Figure 12] Figure 12 is an energy band diagram showing the electronic characteristics of a single layer 4 to which a strong electric field has been applied. [Figure 13] Figure 13 is another energy band diagram showing the electronic properties of a single layer 4 to which a strong electric field has been applied. [Figure 14] Figure 14 is a plan view of an example of a quantum apparatus that does not have the first and second electrodes 6a and 6b. [Figure 15] Figure 15 is a plan view of another example of a quantum device that does not have the first and second electrodes 6a and 6b. [Figure 16] Figure 16 is a cross-sectional view of the quantum device 102b shown in Figure 15 along the XVI-XVI line. [Figure 17] Figure 17 is a process flow diagram showing an example of a manufacturing method for the quantum device 2 shown in Figures 1-3. [Figure 18] Figure 18 is a detailed process flow chart showing an example of a manufacturing method for the quantum device 2 shown in Figures 1-3. [Figure 19] Figure 19 is a cross-sectional view of the manufacturing process shown in Figures 17 and 18. [Figure 20] Figure 20 is a cross-sectional view of the manufacturing process shown in Figures 17 and 18. [Figure 21] Figure 21 is a cross-sectional view of the manufacturing process shown in Figures 17 and 18. [Figure 22] Figure 22 is a cross-sectional view of the manufacturing process shown in Figures 17 and 18. [Figure 23] Figure 23 is a cross-sectional view of the manufacturing process shown in Figures 17 and 18. [Figure 24] Figure 24 is a plan view of another example of a quantum apparatus according to Embodiment 1. [Figure 25]Figure 25 is a cross-sectional view of the quantum device 2m1 shown in Figure 24 along the XXV-XXV line. [Figure 26] Figure 26 is a process flow diagram showing an example of a manufacturing method for the quantum device 2m1. [Figure 27] Figure 27 is a detailed process flow chart showing an example of a manufacturing method for the quantum device 2m1. [Figure 28] Figure 28 is a plan view of another example of a quantum apparatus according to Embodiment 1. [Figure 29] Figure 29 is a cross-sectional view of the quantum apparatus 2m2 shown in Figure 28 along the XXIX-XXIX line. [Figure 30] Figure 30 is a process flow diagram showing an example of a manufacturing method for a quantum device 2m2. [Figure 31] Figure 31 is a detailed process flow chart showing an example of a manufacturing method for a quantum device 2m2. [Figure 32] Figure 32 is a plan view of another example of a quantum apparatus according to Embodiment 1. [Figure 33] Figure 33 is a cross-sectional view of the quantum apparatus 2m3 shown in Figure 32, along the line XXXIII-XXXIII. [Figure 34] Figure 34 is a plan view of an example of a quantum apparatus according to Embodiment 2. [Figure 35] Figure 35 is a cross-sectional view of quantum device 202 shown in Figure 34, along a portion 46a of the XXXV-XXXV line. [Figure 36] Figure 36 is a plan view of another example of a quantum apparatus according to Embodiment 2. [Figure 37] Figure 37 is a cross-sectional view of quantum device 202m shown in Figure 36, along a portion 50a of the XXXVII-XXXVII line. [Figure 38] Figure 38 is a plan view of an example of a quantum apparatus according to Embodiment 3. [Figure 39] Figure 39 is an enlarged view of the area 52 enclosed by the dashed line in Figure 38. [Figure 40] Figure 40 is a cross-sectional view along the XL-XL line shown in Figures 38 and 39. [Figure 41]Figure 41 is a cross-sectional view along the XLI-XLI line shown in Figures 38 and 39. [Figure 42] Figure 42 is a process flow diagram showing an example of a manufacturing method for the quantum device 302. [Figure 43] Figure 43 is a cross-sectional view of the process along the XL-XL line shown in Figure 38. [Figure 44] Figure 44 is a cross-sectional view of the process along the XL-XL line shown in Figure 38. [Figure 45] Figure 45 is a cross-sectional view of the process along the XL-XL line shown in Figure 38. [Figure 46] Figure 46 is a cross-sectional view of the process along the XL-XL line shown in Figure 38. [Figure 47] Figure 47 shows a cross-section of another example of a quantum apparatus according to Embodiment 3. [Figure 48] Figure 48 shows a cross-section of another example of a quantum apparatus according to Embodiment 3. [Modes for carrying out the invention]

[0019] Embodiments of the present invention will be described below with reference to the drawings. However, the technical scope of the present invention is not limited to these embodiments, but extends to the matters described in the claims and their equivalents. Parts having the same structure are denoted by the same reference numerals even if the drawings are different, and their descriptions are omitted.

[0020] (Embodiment 1) (1) Structure Figure 1 is a plan view of an example of a quantum device according to Embodiment 1. Figure 2 is a cross-sectional view along the line II-II shown in Figure 1. Figure 3 is a cross-sectional view along the line III-III shown in Figure 1. The quantum device according to Embodiment 1 is a quantum device having a two-dimensional topological insulator.

[0021] The quantum device 2 shown in Figure 1 has a monolayer 4 of tungsten ditelluride (hereinafter referred to as 1T'-WTe2) having a 1T'-type crystal structure, a first electrode 6a, a second electrode 6b different from the first electrode 6a, and a third electrode 6c connected to the monolayer 4 (see Figures 1-3).

[0022] The quantum device 2 further includes a first coating 8a, partially positioned between the first electrode 6a and the single layer 4; a second coating 8b, partially positioned between the second electrode 6b and the single layer 4; and a support 10 (see Figure 3). Components positioned inside the quantum device 2 (for example, the first electrode 6a) are shown by dashed lines in Figure 1 (the same applies hereafter).

[0023] —Single Layer 4— Single layer 4 is a single layer obtained from a single crystal of tungsten ditelluride having a 1T'-type crystal structure (referred to as single layer 1T'-WTe2 as appropriate) (see "(5) Manufacturing Method"). Single layer 1T'-WTe2 is a two-dimensional topological insulator.

[0024] A monolayer is a layer in a layered material in which atoms are periodically arranged only in the horizontal direction (i.e., the direction parallel to the monolayer) and the vertical direction (i.e., the direction perpendicular to the monolayer). A layered material is a crystal in which multiple monolayers are stacked. Each monolayer in a layered material is bonded to another monolayer located perpendicular to it by weak bonding forces (e.g., van der Waals forces). Tungsten ditelluride is a layered material.

[0025] —Electrodes 6a, 6b, 6c and coatings 8a, 8b— Figure 4 is a plan view showing the portion of the single layer 4 related to the first to third electrodes.

[0026] The first electrode 6a (see Figure 1) applies an electric potential (hereinafter referred to as the first potential) to the first portion 12a (see Figure 4), which is a part of the monolayer 4 and is separated from the outer periphery of the monolayer 4. In the examples shown in Figures 1-3, the first portion 12a is the part located above the first electrode 6a. The outer periphery of the monolayer 4 is hereinafter referred to as the outer periphery of the monolayer.

[0027] On the other hand, the second electrode 6b (see Figure 1) applies an electric potential (hereinafter referred to as the second potential) to the second portion 12b, which is a part of the monolayer 4 and includes a certain area 14 (the area with thick dashed lines drawn over it) on the outer circumference of the monolayer. In the examples shown in Figures 1-3, the second portion 12b is located below the second electrode 6b.

[0028] The first electrode 6a is positioned so that Cooper pairs (see "(3) Operation") generated by the application of a first potential to the first portion 12a can penetrate into the third portion 12c (see Figure 4), which is a part of the second portion 12b and includes a certain range 14 on the outer periphery of the monolayer. Specifically, the first electrode 6a is positioned near the third portion 12c. The third portion 12c is a part of the second portion 12b and is the region where topological superconductivity occurs when Cooper pairs penetrate (see "(3) Operation").

[0029] Figure 5 is a plan view showing the relationship between the outer perimeters of the first electrode 6a, the second electrode 6b, and the single layer 4. Figure 5 also shows a certain range 14 of the single layer outer perimeter 16. The outer perimeter 16a of the first electrode 6a is hereafter referred to as the first outer perimeter. The outer perimeter 16b of the second electrode 6b is hereafter referred to as the second outer perimeter.

[0030] Figure 5 also shows the single layer 4, the first electrode 6a, and the second electrode 6b. However, the single layer 4 and the single layer outer perimeter 16 are represented by the same figure. The same applies to the first electrode 6a and the first outer perimeter 16a, and the same applies to the second electrode 6b and the second outer perimeter 16b.

[0031] The first electrode 6a (see Figure 5) is separated from a certain range 14 on the outer periphery 16 of the single layer in a plan view. In other words, the image obtained by projecting the first electrode 6a onto the single layer 4 is separated from a certain range 14 (the same applies hereafter).

[0032] The first electrode 6a (see Figure 5) further has a first outer perimeter 16a (see Figure 5) that surrounds the first portion 12a (see Figure 4) of the single layer 4 in a plan view. The first portion 12a is, for example, the portion of the first electrode 6a (more precisely, the portion excluding the first outer perimeter 16a) that is projected onto the single layer 4 (the same applies to the second portion 12b). It is clear from the perspective of electromagnetism that the first electrode 6a provides potential not only to this first portion 12a but also to its surroundings (the same applies to the second electrode 6b).

[0033] On the other hand, the second electrode 6b (see Figure 5) has a second outer circumference 16b (see Figure 5) that surrounds the second portion 12b (see Figure 4) of the single layer 4 in a plan view.

[0034] In the example shown in Figure 5, a certain range 14 of the outer perimeter 16 of the single layer extends along the first electrode 6a in a plan view. The shortest distance between the first electrode 6a and the certain range 14 is preferably the shortest distance between the outer perimeter 16 of the single layer and the first electrode 6a.

[0035] The shortest distance d1 between the first electrode 6a and a certain range 14 is preferably 0.5 μm or less. More preferably, the shortest distance d1 is 0.2 μm or less. The distance L (i.e., the leakage distance) over which Cooper pairs generated by electric field-induced superconductivity leak is about 0.5 μm. Therefore, if the shortest distance d1 between the first electrode 6a and the certain range 14 is 0.5 μm or less, Cooper pairs generated in the first part 12a can penetrate into the third part 12c.

[0036] On the other hand, the shortest distance d2 between the portion of the outer periphery 16 of the single layer furthest from a certain range 14 (the upper edge of the single layer 4 in Figure 5) and the first electrode 6a is preferably 1 μm or more, which is sufficiently longer than the leakage distance L. More preferably, the shortest distance d2 is 2 μm or more. In these cases, the Cooper pair cannot penetrate the "furthest portion" mentioned above.

[0037] Figure 4 also shows a portion 15 of the single layer 4, which is different from the first and second portions 12a and 12b. The third electrode 6c is connected to this portion 15 (hereinafter referred to as the contact portion).

[0038] The first potential of the first part 12a is given by the voltage V1 (hereinafter referred to as the first voltage) applied between the first electrode 6a (see Figure 1) and the third electrode 6c. The second potential of the second part 12b (see Figure 4) is given by the voltage V2 (hereinafter referred to as the second voltage) applied between the second electrode 6b (see Figure 1) and the third electrode 6c.

[0039] In the examples shown in Figures 1-3, the first electrode 6a is positioned between the support 10 and the first coating 8a. A first voltage is applied between the first electrode 6a and the third electrode 6c, for example, via a lead wire (not shown) with one end connected to the first electrode 6a. The other end of the lead wire is positioned on an exposed portion of the support 10 (i.e., a portion not covered by the first coating 8a).

[0040] The first and second coatings 8a and 8b (see Figure 3) are preferably hexagonal boron nitride. The thickness of the first and second coatings 8a and 8b is preferably 1 nm to 100 nm. Hexagonal boron nitride is a layered material.

[0041] The first to third electrodes 6a, 6b, and 6c are, for example, elements of Au, Pd, Cu, and Ni, or alloys of these elements. The first electrode 6a may be a laminated film having an adhesive layer in contact with the support 10 and a layer of the element (hereinafter referred to as the element layer). The same applies to the second and third electrodes 6b and 6c.

[0042] The adhesive layer (for example, a Ti layer) adheres the single layer to the substrate (for example, the support 10). The laminated film may have a layer of the alloy instead of the single layer.

[0043] -Support 10- The support 10 includes, for example, a silicon substrate 11 and an insulating film 13 (for example, a silicon oxide film) covering the upper surface of the silicon substrate 11 (see Figure 3). The thickness of the insulating film 13 is preferably 90 to 500 nm.

[0044] The support 10 does not necessarily have an insulating film 13. Although silicon is a semiconductor at room temperature, it is an insulator at the operating temperature of the quantum device 2 (e.g., below 1K). In such cases, the support 10 does not necessarily have an insulating film 13. Alternatively, the support 10 may be an insulating substrate (e.g., a sapphire substrate).

[0045] (2) Physical properties of single layer 4 Figure 6 is a plan view illustrating the physical properties of single layer 4. Since single layer 4 is a two-dimensional topological insulator, it has a bulk 24 with a band gap and an end 26 without a band gap (hereinafter referred to as the single layer end) (see Figure 6). The single layer end 26 is the area that includes the outer periphery of single layer 4 (i.e., single layer outer periphery 16) and surrounds the bulk 24 (hereinafter referred to as the single layer bulk). Therefore, single layer 4 has an insulating single layer bulk 24 and a conductive single layer end 26. The third part 12c, described with reference to Figure 4, is a part of the single layer end 26.

[0046] The single-layer bulk 24 has a valence band and a conduction band separated by a band forbidden zone. On the other hand, as mentioned above, there is no band forbidden zone at the single-layer end 26. Figure 7 is the energy band diagram of single-layer 4 at the single-layer end 26. The horizontal axis is wave number (similar to Figures 8-13). The vertical axis is electron energy (similar to Figures 8-13). Two energy bands EB1 and EB2 (hereinafter referred to as edge bands) are localized at the single-layer end 26. Furthermore, the single-layer end 26 also has a valence band VB and a conduction band CB, similar to the single-layer bulk 24. Since the two edge bands EB1 and EB2 each fill the space between the valence band VB and the conduction band CB, there is no band forbidden zone at the single-layer end 26.

[0047] The edge bands E1 and E2 are one-dimensional bands. The spin of each electron belonging to edge bands EB1 and EB2 is oriented in a specific direction. Specifically, the spin of electrons belonging to one edge band EB1 (hereinafter referred to as the first edge band) is oriented in a direction perpendicular to the monolayer 4. The spin of electrons belonging to the other edge band EB2 (hereinafter referred to as the second edge band) is oriented in the opposite direction to the above unidirectional direction. Therefore, if the spin of an electron belonging to the first edge band EB1 is up-spin, then the spin of an electron belonging to the second edge band EB2 is down-spin.

[0048] In other words, at the monolayer edge 26, there is a pair of one-dimensional bands of spin-polarized electrons. If there are electrons with wave number k1 in the first edge band EB1, then there are electrons with wave number -k in the second edge band EB2.

[0049] Therefore, at the single-layer edge 26, there exists a flow of spin-polarized electrons orbiting the single-layer edge 26 clockwise, and a flow of electrons spin-polarized in the opposite direction orbiting the single-layer edge 26 counterclockwise. These electrons conduct without scattering. This dissipationless conduction state is called the helical edge state.

[0050] When Cooper pairs penetrate a region where helical edge states exist, a superconducting gap opens. This effectively realizes one-dimensional chiral p-wave superconductivity, a type of topological superconductivity (see, for example, Non-Patent Document 1). Therefore, when Cooper pairs penetrate the monolayer edge 26, topological superconductivity occurs.

[0051] (3) Operation Quantum device 2 utilizes the field effect of a single layer 4 to induce topological superconductivity suitable for the generation of Majorana quasiparticle pairs. The generation of Majorana quasiparticle pairs will be described in Embodiment 2.

[0052] (3-1) Single-layer 4 field effect First, let's explain the electric field effect of a single layer 4 (i.e., the effect of the electric field on a single layer 4).

[0053] (3-1-1) Electrical characteristics in a no-field state First, we will explain the electrical characteristics of the single layer 4 when no electric field is applied to it (hereinafter referred to as the no-electric-field state). Figures 8 and 9 are energy band diagrams showing the electronic characteristics of the single layer 4 when no electric field is applied. Figure 8 shows the energy band at the single layer end 26. Figure 9 shows the energy band at the single layer bulk 24.

[0054] Figures 8 and 9 show energy bands covering a wider range than that in Figure 7 (the same applies to Figures 10-13). The monolayer edge 26 has third to sixth edge bands EB3, EB4, EB5, and EB6, in addition to the first and second energy bands EB1 and EB2 described with reference to Figure 7 (see Figure 8). The third to sixth edge bands, like the first and second edge bands EB1 and EB2, are spin-polarized one-dimensional bands localized at the monolayer edge 26.

[0055] The third and fourth edge bands EB3 and EB4 are spin-polarized one-dimensional bands whose lowest energy is higher than the bottom of the conduction band CB. On the other hand, the fifth and sixth edge bands EB5 and EB6 are spin-polarized one-dimensional bands whose highest energy is lower than the top of the valence band VB.

[0056] The spin direction of electrons belonging to the third and fifth edge bands EB3 and EB5 is opposite to that of electrons belonging to the first edge band EB1. On the other hand, the spin direction of electrons belonging to the fourth and sixth edge bands EB4 and EB6 is opposite to that of electrons belonging to the second edge band EB2.

[0057] In a field-free state, the Fermi level E in single-layer bulk 24 F It lies between the valence band VB and the conduction band CB (see Figure 9). Therefore, the single-layer bulk 24 is insulating.

[0058] Fermi level E at single-layer end 26 F(See Figure 8) The first and second edge bands EB1 and EB2 cross between the valence band VB and the conduction band CB. Therefore, the conduction state of the single-layer edge 26 is conductive. This conduction state is the dissipationless helical edge state described above.

[0059] As described above, when no electric field is applied to the single layer 4, the single layer bulk 24 is insulating, and a non-dissipating helical edge state exists at the single layer end 26. These electrical characteristics appear when the temperature of the single layer 4 is 100K or less.

[0060] (3-1-2) Field effect in weak electric field conditions Figures 10 and 11 are energy band diagrams showing the electronic properties of the single layer 4 to which a weak electric field is applied. Figure 10 shows the energy band at the single layer edge 26. Figure 11 shows the energy band at the single layer bulk 24.

[0061] However, the electric field is applied to only a portion of the single layer, not the entire single layer (the same applies in the next section). In this and the next section, to avoid redundant explanations, the portion of the single-layer bulk 24 to which the electric field is applied will simply be referred to as "single-layer bulk 24". The same applies to the portion of the single-layer end 26 to which the electric field is applied.

[0062] In a weak electric field state (i.e., a weak electric field is applied to single layer 4), the Fermi level E in single layer bulk 24 is F This is slightly higher than the bottom of the conduction band CB (see Figure 11). As a result, the single-layer bulk 24 becomes normally conductive.

[0063] Fermi level E at single-layer end 26 F (See Figure 10) The first and second edge bands EB1 and EB2 are crossed, just as in the no-field state. However, even at the single-layer end 26, the Fermi level E F This is slightly higher than the bottom of the conduction band CB. Therefore, at the monolayer edge 26, there are electrons belonging to the first edge band EB1, electrons belonging to the second edge band EB2, and electrons belonging to the conduction band CB.

[0064] Electrons belonging to the first and second edge bands E1 and E2 cause dissipationless conduction. Therefore, even under weak electric field conditions, a helical edge state exists at the monolayer edge 26. On the other hand, electrons belonging to the conduction band CB cause normal conduction, with each electron moving while being scattered.

[0065] As described above, when Cooper pairs enter the first and second edge bands E1 and E2, a superconducting gap opens at the Fermi level. As a result, topological superconductivity is effectively realized. However, in a weak field state, electrons may move from the first and second edge bands EB1 and EB2 to the conduction band CB. Furthermore, the reverse movement also occurs. Therefore, electrons present at the monolayer edge 26 in a weak field state are scattered while they belong to the conduction band CB.

[0066] Therefore, topological superconductivity arising from helical edge states under weak electric field conditions is not suitable for generating Majorana quasiparticle pairs. This is because Majorana quasiparticle pairs generated from such topological superconductivity are short-lived due to the aforementioned scattering.

[0067] As described above, when a weak electric field is applied to the single layer 4, the single layer bulk 24 becomes a normal conductor. On the other hand, even under weak electric field conditions, a helical edge state exists at the single layer end 26. However, this helical edge state is not suitable for the generation of Majorana quasiparticle pairs.

[0068] (3-1-3) Field effects in strong electric field conditions Figures 12 and 13 are energy band diagrams showing the electronic characteristics of the single layer 4 to which a strong electric field (more precisely, an electric field stronger than the "weak electric field" described above) is applied. Figure 12 shows the energy band at the single layer edge 26. Figure 13 shows the energy band in the single layer bulk 24.

[0069] In a strong electric field state (i.e., a strong electric field is applied to single layer 4), the Fermi level E FThe energy difference between the conduction band CB and the bottom expands (see Figures 12 and 13). As a result, the single-layer bulk 24 enters a superconducting state (more precisely, a state in which S-wave superconductivity occurs). That is, field-induced superconductivity occurs. Consequently, Cooper pairs are generated in the single-layer bulk 24.

[0070] Even at the single-layer end 26, the Fermi level E F The energy difference between this and the bottom of the conduction band CB expands (see Figure 12). Then, the Fermi level E F It crosses not only the first and second edge bands EB1 and EB2, but also the third and fourth edge bands EB3 and EB4.

[0071] As a result, under a strong electric field, electrons are distributed into four spin-polarized one-dimensional bands. In this case, the conditions for the appearance of Majorana quasiparticle pairs (i.e., the Majorana condition) are not met. Therefore, under a strong electric field, Majorana quasiparticle pairs do not arise from topological superconductivity at the monolayer edge 26.

[0072] As described above, when a strong electric field is applied to the single layer 4, S-wave superconductivity is induced in the single-layer bulk 24, and Cooper pairs are generated. On the other hand, the conditions for the appearance of Majorana quasiparticle pairs are no longer met at the single-layer edge 26.

[0073] (3-2) Operating temperature The temperature at which field-induced superconductivity occurs in single layer 4 is below 1K (see, for example, Non-Patent Documents 3-6). Therefore, the operating temperature of quantum device 2 is below 1K.

[0074] (3-3) Induction of topological superconductivity Applying appropriate potentials to the first and second parts induces topological superconductivity suitable for the generation of Majorana quasiparticle pairs. Here, we describe how to appropriately apply the first and second potentials.

[0075] (3-3-1) Assignment of the first potential The first electrode 6a provides a potential to the first part 12a (see Figure 4) at which field-induced superconductivity occurs (see "(3-1-3) Field Effect in Strong Field Conditions"). In other words, the first electrode 6a provides the first potential to the first part 12a at which Cooper pairs are generated.

[0076] Specifically, when the thickness of the first coating 8a is 6 to 12 nm, a voltage of, for example, 3 to 4 V (hereinafter referred to as the first voltage) is applied between the first electrode 6a (see Figure 1) and the third electrode 6c. However, the first coating 8a is hexagonal boron nitride.

[0077] The first voltage V1 is applied such that the potential of the first electrode 6a is higher than the potential of the third electrode 6c. If the potential of the first electrode 6a is φ1 and the potential of the third electrode 6c is φ3, then V1 = φ1 - φ3.

[0078] When the first voltage V1 is positive, the Fermi level in the first section 12a rises relative to the conduction band CB.

[0079] (3-3-2) Application of the second potential The second electrode 6b provides a second potential lower than the first potential to the second portion 12b (see Figure 4). As a result, the helical edge state in the third portion 12c becomes suitable for the generation of Majorana quasiparticle pairs.

[0080] Specifically, a voltage lower than the first voltage V1 (for example, 3-4V) (hereinafter referred to as the second voltage) is applied between the second electrode 6b (see Figure 1) and the third electrode 6c. As a result, the second portion 12b is given a second potential lower than the first potential by the second electrode 6b.

[0081] The first electrode 6a is positioned near the third portion 12c (see "(1) Structure"). Therefore, when a first voltage V1 (>0) is applied between the first electrode 6a and the third electrode 6c, not only the first potential of the first portion 12a but also the potential of the third portion 12c rises to some extent.

[0082] Then, the Fermi level Ef in the third part 12c rises to some extent relative to the conduction band CB. When this rise causes the Fermi level Ef to become higher than the bottom of the conduction band, the helical edge state in the third part 12c becomes unsuitable for the generation of Majorana quasiparticle pairs (see "(3-1-2) Field Effects in Weak Field States").

[0083] Therefore, in order to suppress the rise in the Fermi level Ef in the third section 12c, a second voltage V2 (e.g., -1 to 1V) lower than the first voltage V1 is applied between the second electrode 6b and the third electrode 6c. As a result, the helical edge state in the third section 12c becomes suitable for the generation of Majorana quasiparticle pairs (see "(3-1-1) Electrical characteristics in the field-free state").

[0084] If the potential of the second electrode 6a is φ2 and the potential of the third electrode 6c is φ3, then V2 = φ2 - φ3. The values ​​exemplified as the first voltage V1 (i.e., 3~4V) and the values ​​exemplified as the second voltage V2 (i.e., -1~1V) are appropriate when the second coating 8b is hexagonal boron nitride with a thickness of 6~12 nm.

[0085] (3-3-3) Induction of topological superconductivity Finally, we will explain the process by which topological superconductivity occurs.

[0086] The Cooper pairs generated by applying a first potential to the first section 12a leak out of the first section 12a and then penetrate into the third section 12c. The third section 12c is a part of the monolayer end 26 where the helical edge state exists. Therefore, when Cooper pairs penetrate into the third section 12c, a superconducting gap opens at the Fermi level. As a result, topological superconductivity occurs.

[0087] As is clear from the above explanation, the Cooper pairs generated in the first portion 12a penetrate from the first portion 12a to the third portion 12c only through the monolayer 4. Therefore, according to Embodiment 1, it becomes possible to inject Cooper pairs into the monolayer end 26 without passing through a heterointerface.

[0088] Furthermore, according to Embodiment 1, the Fermi level of the third portion 12c can be controlled by the second potential supplied to the second portion 12b by the second electrode 6b. By appropriately controlling this Fermi level, it becomes possible to induce topological superconductivity suitable for the generation of Majorana quasiparticle pairs.

[0089] (4) Comparative Example (4-1) Comparative Example 1 Figure 14 is a plan view of an example of a quantum device that does not have first and second electrodes 6a, 6b. The quantum device 102a shown in Figure 14 has a support 110 (e.g., a silicon substrate) and a single layer 4 (i.e., single layer 1T'-WTe2) placed on the support 110. The quantum device 102a further has a superconductor 128a (e.g., aluminum) covering a portion of the single layer end 26 (see Figure 6).

[0090] When the quantum device 102a is cooled to near absolute temperature (for example, below 1K), it is expected that Cooper pairs will penetrate the monolayer edge 26 through the heterointerface between the superconductor 128a and the monolayer 4. However, during the manufacturing process of the quantum device 102a, an oxide film is formed between the superconductor 128a and the monolayer 4. This oxide film suppresses the penetration of Cooper pairs into the monolayer edge 26.

[0091] The quantum device 102a is manufactured, for example, by following the procedure below. First, a single layer 4 is separated from a 1T'-WTe2 single crystal in a glove box filled with an inert gas. Next, this single layer 4 is placed on a support 110. Then, a photoresist film is formed on the single layer 4 and the support 110.

[0092] Subsequent steps are difficult to perform inside the glove box. Therefore, the support 110 on which the photoresist film is formed is removed from the glove box filled with inert gas. Next, openings (hereinafter referred to as resist openings) are formed in the photoresist film on the single layer 4 and the support 110, partially exposing the outer periphery of the single layer 4.

[0093] Next, a superconducting film (e.g., an Al film) is deposited on top of the photoresist film and inside the resist openings. Finally, the lift-off of this superconducting film forms a superconductor 128a that partially covers the monolayer end 26.

[0094] When a resist opening is formed, the single layer 4 within the formed resist opening (hereinafter referred to as the single-layer exposed portion) is exposed to the atmosphere. As a result, an oxide film of the single layer 4 is formed on this single-layer exposed portion. This oxide film persists even after the completion of the quantum device 102a, suppressing the penetration of Cooper pairs into the single-layer edge 26.

[0095] On the other hand, in the quantum apparatus 2 according to Embodiment 1, Cooper pairs are generated in the second portion 12a within the monolayer 4, and then penetrate to the monolayer end 26 via the monolayer 4. That is, Cooper pairs penetrate to the monolayer end 26 (more precisely, the third portion 12c) without passing through a heterointerface. Therefore, in the quantum apparatus 2 according to Embodiment 1, there are no obstacles that suppress the penetration of Cooper pairs into the monolayer end 26.

[0096] Incidentally, a built-in potential is formed in a portion of the monolayer 4 that is covered by the superconductor 128a (hereinafter referred to as the junction). Due to this built-in potential, the Fermi level of the junction may rise above the bottom of the conduction band. This rise in the Fermi level is undesirable because it shortens the lifetime of Majorana quasiparticle pairs generated from topological superconductivity (see "(3-1-2) Field Effects in Weak Field States").

[0097] On the other hand, the quantum apparatus 2 according to Embodiment 1 has a second electrode 6b (see Figure 1) that provides a second potential to the second part 12b (see Figure 4). Therefore, the quantum apparatus 2 according to Embodiment 1 can solve the problem caused by the elevation of the Fermi level (see "(3-3-2) Provision of the second potential"). The same applies to the quantum apparatus 102b according to Comparative Example 2, which will be described later.

[0098] Furthermore, oxidation of the single layer 4 occurs not only when forming resist openings, but also when forming the superconductor 128a due to the lift-off of the superconductor film. At this time, most of the single layer 4 is oxidized. As a result, the single layer 4 ceases to be a two-dimensional topological insulator. On the other hand, the quantum device 2 according to Embodiment 1 does not have this problem because it has first and second coatings 8a and 8b that seal the single layer 4.

[0099] (4-2) Comparative Example 2 Figure 15 is a plan view of another example of a quantum device without the first and second electrodes 6a,6b. Figure 16 is a cross-sectional view of the quantum device 102b shown in Figure 15 along the line XVI-XVI.

[0100] The quantum device 102b comprises a support 110 and a superconductor 128b (e.g., aluminum) disposed on the support 110. The quantum device 102b further comprises a single layer 4 that partially covers the outer periphery of the superconductor 128b and a coating 108 that covers the single layer 4. The coating 108 is, for example, hexagonal boron nitride.

[0101] Unlike quantum device 102a shown in Figure 14, quantum device 102b has a coating 108 covering the monolayer 4. Therefore, oxidation of monolayer 4 is suppressed. However, during the manufacturing process of quantum device 102b, an oxide film is formed between the superconductor 128b and the monolayer 4. This oxide film suppresses the penetration of Cooper pairs into the monolayer edge 26.

[0102] The quantum device 102b is manufactured, for example, by following the procedure below. First, a superconducting film (e.g., an aluminum film) is deposited on a support 110 using a vacuum deposition apparatus. Next, the support 110 on which the superconducting film has been deposited is removed from the vacuum deposition apparatus. Subsequently, the superconducting film on the support 110 is shaped, for example, by photolithography and dry etching to form a superconductor 128b.

[0103] Separately from these processes, the single layer 4 is separated from the 1T'-WTe2 single crystal in a glove box filled with inert gas. Next, the upper surface of the separated single layer 4 is attached to the coating 108. Finally, the single layer 4 attached to the coating 108 is placed on the support 110 so that the single layer 4 partially covers the outer periphery of the superconductor 128b.

[0104] When the support 110 on which the superconducting film is deposited is removed from the vacuum deposition apparatus, the surface of the superconducting film is covered with an oxide film. This oxide film persists even after the completion of the quantum device 102b, suppressing the penetration of Cooper pairs into the single-layer edge 26. On the other hand, such an oxide film does not exist in the quantum device 2 according to Embodiment 1.

[0105] (5) Manufacturing method Figures 17 and 18 are process flow diagrams showing an example of a manufacturing method for the quantum device 2 shown in Figures 1-3. Figure 18 shows details of the manufacturing method shown in Figure 17. Figures 19-23 are cross-sectional view steps of the manufacturing method shown in Figures 17 and 18.

[0106] (4-1) First step S1 (see Figure 17) First, the first surface of the single layer 4 separated from the 1T'-WTe2 single crystal is covered with a first coating 8a, and then the second surface of the single layer 4 is covered with a second coating 8b (see Figures 3 and 17). Preferably, the single layer 4 is separated from the 1T'-WTe2 single crystal in a space where the atmosphere is removed, and then placed in a space where the atmosphere is removed until the first step S1 is completed. A "space where the atmosphere is removed" is, for example, the inside of a glove box filled with an inert gas.

[0107] Specifically, a composite film is formed having a hexagonal boron nitride thin (hereinafter referred to as the first h-BN thin), a single layer 4, and another hexagonal boron nitride thin (hereinafter referred to as the second h-BN thin) in this order (step S1a in Figure 18).

[0108] For details, first, the first h-BN thin film 30a is separated from the hexagonal boron nitride single crystal by the adhesive tape method (see "-Adhesive Tape Method-") and attached to the first substrate 32a (see Figure 19(a)). The first substrate 32a is a substrate having a silicon substrate 34 and an SiO2 film 36 covering the surface of this silicon substrate 34a (the same applies to the second substrate 32b and the third substrate 32c described later).

[0109] Subsequently, the first substrate 32a to which the first h-BN thin film 30a is attached is placed in a glove box filled with an inert gas (e.g., argon gas). The first h-BN thin film 30a is an example of the first coating 8a (see Figure 3).

[0110] Furthermore, the second h-BN thin film 30b is separated from the hexagonal boron nitride single crystal by the adhesive tape method and attached to the second substrate 32b (see Figure 19(b)). Subsequently, the second substrate 32b with the second h-BN thin film 30b attached is stored in the glove box. The second h-BN thin film 30b is an example of the second coating 8b (see Figure 3).

[0111] The separation and attachment of the first h-BN flake 30b may be carried out in a glove box filled with inert gas. The same applies to the separation and attachment of the second h-BN flake 30b.

[0112] Furthermore, within the glove box filled with inert gas, the single layer 4 is separated from the 1T'-WTe2 single crystal by the adhesive tape method and attached to the third substrate 32c (see Figure 19(c)).

[0113] Finally, for example, by a stamping method, the single layer 4 and the first h-BN 30a are attached to the second h-BN thin layer 30b in that order. This yields a composite film 38 (see Figure 20(b)) having the first h-BN thin layer 30a, the single layer 4, and the second h-BN thin layer 30b in that order.

[0114] From here, we will explain the procedure for forming the composite film 38 by the stamping method. First, a stamp 44 is formed having a transparent, highly elastic, dome-shaped synthetic resin 40 (hereinafter referred to as the dome) and a slide glass 42 to which the dome 40 is attached (see Figure 20(a)). The dome 40 is, for example, polydimethylsiloxane. Then, a thin film of polyvinyl chloride (hereinafter referred to as the polyvinyl chloride film), which is not shown, is attached to the dome 40. Instead of the polyvinyl chloride film, a thin film of another thermoplastic resin (for example, polycarbonate) may be used.

[0115] Next, the dome 40, to which the polyvinyl chloride film is attached, is pressed against the second h-BN thin film 30b (see Figure 19(b)), which has been heated to 65-75°C. This heats the polyvinyl chloride film between the second h-BN thin film 30b and the dome 40, increasing their adhesive force. As a result, the second h-BN thin film 30b adheres to the dome 40. After that, the stamp 44 is pulled away from the second substrate 32b. The second h-BN thin film 30b is then peeled off the second substrate 32b while still attached to the dome 40.

[0116] Furthermore, the second h-BN flake 30b attached to the dome 40 is pressed against the single layer 4 (see Figure 19(c)) which has been heated to 65-75°C. As a result, the single layer 4 adheres to the second h-BN flake 30b. After that, the stamp 44 is pulled away from the third substrate 32c. As a result, the single layer 4 is peeled off from the third substrate 32c while still attached to the second h-BN flake 30b.

[0117] Thin sections separated from single crystals of layered materials have extremely flat surfaces. When such thin sections are brought into contact with each other, they adhere to one another. Since hexagonal boron nitride and 1T'-WTe2 are layered materials, single layer 4 adheres to the second h-BN thin section 30b.

[0118] Finally, the single layer 4 attached to the second h-BN thin layer 30b is pressed against the first h-BN thin layer 30a (see Figure 19(a)), which has been heated to 65-75°C. The first h-BN thin layer 30a then adheres to the single layer 4. After that, the stamp 44 is pulled away from the third substrate 32c. The first h-BN thin layer 30a is then peeled off the first substrate 32a while still attached to the single layer 4.

[0119] As a result, a composite film 38 (see Figure 20(b)) is obtained having a first h-BN thin film 30a, a single layer 4, and a second h-BN thin film 30b in that order.

[0120] Through these steps, the single layer 4 is sealed by the first and second h-BN thin layers 30a and 30b. Therefore, even if the single layer 4 is removed from the glove box after this, it will not be oxidized by the atmosphere.

[0121] The film thickness of the first and second h-BN thin films 30a and 30b is preferably 1 to 100 nm. More preferably, the film thickness of the first and second h-BN thin films 30a and 30b is 10 to 20 nm.

[0122] If the film thickness of the first and second h-BN thin films 30a and 30b is 100 nm or less, the first and second h-BN thin films 30a and 30b will bend and reliably seal the single layer 4. Furthermore, if the film thickness of the first and second h-BN thin films 30a and 30b is 1 nm or more, the first and second h-BN thin films 30a and 30b will block the atmosphere and suppress oxidation of the single layer 4.

[0123] —Adhesive Tape Method— The adhesive tape method is a method for obtaining thin slices of layered material from single crystals of that material using adhesive tape. First, separate adhesive tapes are attached to the front and back surfaces of the single crystal of the layered material. Next, these adhesive tapes are pulled apart to cleave the layered material. Furthermore, the thinned layered material is cleaved again using adhesive tape. By repeating this re-cleaving process, an extremely thin layered material (i.e., a thin slice) is obtained. At this stage, the thin slice of layered material remains attached to the adhesive tape.

[0124] Next, the thin piece attached to the adhesive tape is pressed against the substrate (for example, the first substrate 32a). Finally, the adhesive tape with the piece attached is pulled away from the substrate. At this time, the final cleavage occurs, and an even thinner piece (for example, the first h-BN piece 30a) is left behind on the substrate.

[0125] (4-2) Second process S2 (see Figure 17) After the first step S1, a first electrode 6a is obtained that is in contact with the first coating 8a (here, the first h-BN thin film 30a) (see Figures 3 and 21(b)). At this time, the first electrode 6a is obtained such that, in a plan view, the first electrode 6a is separated from a certain range 14 of the outer circumference 16 of the single layer, and in a plan view, the first outer circumference 16a of the first electrode 6a surrounds a part of the single layer 4 (see Figure 5).

[0126] Specifically, first, a first electrode 6a is formed on the support 10 (step S2a in Figure 18). Then, a composite film 38 is attached to the support 10 on which the first electrode 6a is formed (step S2b in Figure 18).

[0127] In detail, first, a photoresist film having an opening substantially contiguous with the first electrode 6a in a plan view is formed on the support 10. Next, titanium (Ti) and gold (Au) are deposited in that order on top of this photoresist film and inside the opening. Subsequently, the first electrode 6a is formed by the lift-off of the titanium and gold (see Figure 21(a)).

[0128] Next, the support 10 on which the first electrode 6a is formed is heated to 125-135°C. Then, the composite film 38 (see Figure 20(b)) is pressed against the surface of the support 10 so that the first h-BN flake 30a is in contact with it. As a result, the first h-BN flake 30a (i.e., the first coating 8a) that covers the first surface of the single layer 4 adheres to the support 10. The composite film 38 is pressed against the support 10 in such a way that, in a plan view, the first electrode 6a is surrounded by the outer periphery 16 of the single layer.

[0129] Finally, the stamp 44 is pulled away from the support 10. The composite film 38 is then peeled off from the stamp 44 and left on the support 10 (see Figure 21(b)). As a result, a first electrode 6a is obtained that is in contact with the first h-BN thin film 30a (in this case, the first coating 8a).

[0130] When the polyvinyl chloride film that adheres the 2h-BN thin film 30b to the dome 40 is heated to approximately 120°C or higher, the adhesive strength of the polyvinyl chloride film decreases. Therefore, when the composite film 38 is pressed against the support 10 heated to 125-135°C, the composite film 38 peels off from the stamp 44 and is left behind on the support 10.

[0131] (4-3) Third step S3 (see Figure 17) After the second step S2, a second electrode 6b is obtained that is in contact with the second coating 8b (here, the second h-BN thin film 30b) (see Figures 3 and 22(a)). At this time, the second electrode 6b is obtained such that, in a plan view, a certain area 14 of the outer circumference 16 of the single layer is surrounded by the second outer circumference 16b of the second electrode 6b (see Figure 5).

[0132] Specifically, the second electrode 6b is formed on the composite film 38 (see Figure 21(b)) (step S3a in Figure 18).

[0133] First, a photoresist film is formed on the second h-BN thin film 30b, having an opening that surrounds a certain area 14 of the outer periphery 16 of the single layer in a plan view. Next, titanium and gold are deposited in this order on top of the photoresist film and inside the opening. Finally, the lift-off of the titanium and gold forms the second electrode 6b (see Figure 22(a)). As a result, a second electrode 6b is obtained that is in contact with the second h-BN thin film 30b (here, the second coating 8b).

[0134] (4-4) Fourth step S4 (see Figure 17) After the third step S3, a third electrode 6c is obtained that is in contact with a portion of the single layer 4 (see Figures 2 and 23).

[0135] Specifically, first, through-holes reaching the single layer 4 are formed in the composite film 38 (step S4a in Figure 18). Then, a third electrode 6c that is in contact with the single layer 4 is formed within these through-holes (step S4b in Figure 18).

[0136] For details, first, a photoresist film having an opening above the contact portion 15, as explained with reference to Figure 4, is formed on the 2h-BN30b and the support 10. Next, the 2h-BN30b is etched through this opening by reactive ion etching until the contact portion 15 is exposed. This etching forms a through-hole 46 that reaches the single layer 4 (see Figure 22(b)). Subsequently, titanium and gold are deposited in that order on top of the photoresist film and inside the through-hole 46. Finally, the lift-off of the titanium and gold forms the third electrode 6c (see Figure 23). As a result, a third electrode 6c that contacts the contact portion 15 of the single layer 4 is obtained.

[0137] (6) Variant (6-1) Torture 1 Figure 24 is a plan view of another example of a quantum apparatus according to Embodiment 1 (hereinafter referred to as Modification 1). Figure 25 is a cross-sectional view of the quantum apparatus 2m1 shown in Figure 24 along the line XXV-XXV. Quantum apparatus 2m1 is similar to quantum apparatus 2 illustrated in Figures 1-3. Therefore, the parts common to quantum apparatus 2 will not be explained.

[0138] In the quantum apparatus 2 illustrated in Figure 1, the first electrode 6a and the first coating 8a are in contact with the support 10 (see Figure 3). On the other hand, in the quantum apparatus 2m1 shown in Figures 24 and 25, the second electrode 6b and the second coating 8b are in contact with the support 10.

[0139] The quantum devices 2 and 2m1 illustrated in Figures 1 and 24 operate independently of the support 10. Therefore, quantum device 2m1, like quantum device 2, enables the injection of Cooper pairs into the monolayer end 26 (see Figure 6) without a heterointerface and the control of the Fermi level at the monolayer end 26. Modification 1 increases the variations of the quantum device according to Embodiment 1.

[0140] -Manufacturing method- Figures 26 and 27 are process flow diagrams showing an example of a manufacturing method for the quantum device 2m1. Figure 27 shows details of the manufacturing method shown in Figure 26.

[0141] Some of the processes shown in Figure 27 (for example, step S1a) are enclosed in dashed lines. The processes enclosed in dashed lines are the processes explained based on Figure 18. Therefore, the explanation of these processes is omitted (and so on).

[0142] As shown in Figure 26, the manufacturing method for quantum device 2m1 is similar to the manufacturing method for quantum device 2 (see Figure 17). However, in the manufacturing method for quantum device 2m1, the second step S2 is performed after the third step S3. Otherwise, the manufacturing method shown in Figure 26 is substantially the same as the manufacturing method shown in Figure 17.

[0143] Specifically, first, step S1a (see Figure 27) is performed to form the composite film 38. Next, instead of step S2a (see Figure 18) to form the first electrode 6a on the support 10, a second electrode 6a (see Figure 25) is formed on the support 10 (step S3b in Figure 27). Figure 18 is a process flow diagram showing the details of the manufacturing method shown in Figure 17.

[0144] After step S3b, the composite film 38 is attached to the support 10 (step S3c). Specifically, the second coating 8b (see Figure 25), which covers the second surface of the single layer 4, is attached to the support 10 on which the second electrode 6b is formed. At this time, in a plan view, the second coating 8b is attached to the support 10 such that the outer circumference 16b of the second electrode 6b surrounds a certain area 14 of the outer circumference 16 of the single layer (see Figure 5). This results in a second electrode 6b that is in contact with the second coating 8b.

[0145] In Modification 1, the first h-BN thin layer 30a (i.e., the bottom layer of the composite film 38) is the second coating 8b (i.e., the electrode in contact with the second electrode 6b). On the other hand, the second h-BN thin layer 30b (i.e., the top layer of the composite film 38) is the first coating 8a (i.e., the electrode in contact with the first electrode 6a) (see Figures 20(b) and 25).

[0146] Next, instead of step S3a (see Figure 18) in which the second electrode 6b is formed on the composite film 38, the first electrode 6a is formed on the composite film 38 (step S2c). Specifically, in a plan view, the first electrode 6a is formed on the first coating 8a such that, for example, the first electrode 6a is surrounded by the outer periphery 16 of the single layer (see Figure 5). This provides a first electrode 6a that is in contact with the first coating 8a.

[0147] Finally, steps S4a and S4b are performed to complete the quantum apparatus 2m2.

[0148] The process from step S3b to step S3c is an example of the third process S3 (see Figure 26). Step S2c is an example of the second process S2.

[0149] (6-2) Modification 2 Figure 28 is a plan view of another example of a quantum apparatus according to Embodiment 1 (hereinafter referred to as Modification 2). Figure 29 is a cross-sectional view of the quantum apparatus 2m2 shown in Figure 28 along the line XXIX-XXIX. Quantum apparatus 2m2 is similar to quantum apparatus 2 illustrated in Figure 1. Therefore, the parts common to quantum apparatus 2 will not be explained.

[0150] In the quantum apparatus 2 illustrated in Figure 1, the first electrode 6a and the second electrode 6b are in contact with separate coatings (see Figure 3). On the other hand, in the quantum apparatus 2m2 shown in Figures 28 and 29, the first electrode 6a and the second electrode 6b are in contact with the same coating (see Figure 29). In other words, the second coating 8b in contact with the second electrode 6b is the same coating as the first coating 8a in contact with the first electrode 6a.

[0151] The quantum apparatus 2 shown in Figure 1 and the quantum apparatus 2m2 shown in Figure 28 operate regardless of whether the first and second electrodes 6a and 6b are in contact with the same coating. Therefore, the quantum apparatus 2m2, like the quantum apparatus 2, enables the injection of Cooper pairs into the monolayer end 26 (see Figure 6) without a heterointerface, and the control of the Fermi level at the monolayer end 26. Modification 2 increases the variations of the quantum apparatus according to Embodiment 1.

[0152] As shown in Figure 29, the quantum device 2m2 has a third coating 8c in contact with the support 10. However, even without the third coating 8c, the single layer 4 is sealed by the support 10 and the first coating 8a (i.e., the second coating 8b). Therefore, the quantum device 2m2 does not need to have the third coating 8c.

[0153] -Manufacturing method- Figures 30 and 31 are process flow diagrams showing an example of a manufacturing method for a quantum device 2m2. Figure 31 shows details of the manufacturing method shown in Figure 30.

[0154] As shown in Figure 30, the manufacturing method for quantum device 2m2 is similar to the manufacturing method for quantum device 2 (see Figure 17). However, in the manufacturing method for quantum device 2m2, the second coating 8b is the same coating as the first coating 8a. Therefore, the second surface (one surface of the single layer 4) covered by the second coating 8b is the same surface as the first surface (another surface of the single layer 4) covered by the first coating 8a. Furthermore, the second step S2 and the third step S3 are integrated into a single step (hereinafter referred to as step S2 / 3). Aside from these, the manufacturing method shown in Figure 30 is substantially the same as the manufacturing method shown in Figure 17.

[0155] Specifically, first, step S1a (see Figure 31) is performed to form the composite film 38. Next, step S2a (see Figure 18) to form the first electrode 6a on the support 10 is omitted, and the composite film 38 (see Figure 20(b)) is directly attached to the support 10 (step S2 / 3a in Figure 31).

[0156] After step S2 / 3a, the first electrode 6a and the second electrode 6b are formed on the composite film 38, for example by lift-off (step S2 / 3b in Figure 30). This provides the first electrode 6a in contact with the first coating 8a and the second electrode 6b in contact with the second coating 8b.

[0157] In modified example 2, the second h-BN thin layer 30b (i.e., the uppermost layer of the composite film 38) is the first coating 8a in contact with the first electrode 6a (see Figure 29) and the second coating 8b in contact with the second electrode 6b (see Figure 29). The first h-BN thin layer 30a (i.e., the lowermost layer of the composite film 38) is the third coating 8c in contact with the support 10 (see Figure 29).

[0158] Finally, steps S4a and S4b are performed to complete the quantum apparatus 2m2.

[0159] The process from step S2 / 3a to step S2 / 3b is an example of step S2 / 3 (see Figure 30), in which the second process S2 and the third process S3 are integrated into one.

[0160] In the example shown in Figures 30-31, the first and second electrodes 6a and 6b are formed on the composite film 38. However, the first and second electrodes 6a and 6b may also be formed on the support 10.

[0161] (6-3) Modification example 3 Figure 32 is a plan view of another example of a quantum apparatus according to Embodiment 1 (hereinafter referred to as Modification 3). Figure 33 is a cross-sectional view of the quantum apparatus 2m3 shown in Figure 32 along the line XXXIII-XXXIII. Quantum apparatus 2m3 is similar to quantum apparatus 2 illustrated in Figures 1-3. Therefore, the parts common to quantum apparatus 2 will not be explained.

[0162] In the quantum apparatus 2 illustrated in Figure 1, the second electrode 6b is a metal film formed on the second coating 8b in contact with the single layer 4 (see Figure 3). On the other hand, in the quantum apparatus 2m3 shown in Figures 32 and 33, the second electrode 6b is the silicon substrate 11 of the support 10. The silicon substrate 11 preferably has a high concentration (for example, 1 × 10⁻¹⁶).18 cm 3 It is a degenerate semiconductor having impurities of the above).

[0163] The second film 8b, a part of which is disposed between the second electrode 6b (that is, the silicon substrate 11) and the single layer 4, is the same film as the first film 8a with which the first electrode 6a contacts (see FIG. 33).

[0164] By applying a voltage between the first electrode 6a and the third electrode 6c, a potential can be applied to a part of the single layer 4 above the first electrode 6a (that is, the first part 12a). Further, by applying a voltage between the silicon substrate 11 (that is, the second electrode 6b) and the third electrode 6c, a potential can be applied to a range of the single layer 4 that does not include the first part 12a. This range is an example of a second part including a certain range 14 of the single layer outer periphery 16. That is, the quantum device 2m3 has a first electrode 6a that applies a first potential to the first part 12a and a second electrode 6b that applies a second potential to the second part.

[0165] Therefore, like the quantum device 2, the quantum device 2m3 can also inject Cooper pairs into the single layer end portion 26 (see FIG. 6) without passing through a heterointerface and control the Fermi level at the single layer end portion 26. According to the third modification, the variations of the quantum device according to the first embodiment increase.

[0166] - Manufacturing method - The quantum device 2m3 can be formed, for example, by omitting step S3a of forming the second electrode 6b on the composite film 38 in the manufacturing method shown in FIG. 18.

[0167] In the examples shown in FIGS. 32 to 33, the first electrode 6a is formed on the support 10. However, the first electrode 6a may be formed on a film 8d (that is, the uppermost layer of the composite film 38) covering the single layer 4. In this case, the first part 12a (see FIG. 4) to which the first electrode 6a applies a potential is between the first electrode 6a and the second electrode 6b (that is, the silicon substrate 11). Therefore, the first electrode 6a cooperates with the second electrode 6b to apply the potential of the first part 12a.

[0168] In the manufacturing method described so far, the first step is the first step S1 (see Figures 17, 26, and 30), in which the single layer 4 is covered with the first film 8a and the second film 8b. However, the first step S1 may be performed at any time before the composite film 38 (see Figure 20(b)) is attached to the support 10. The first step S1 (i.e., step S1a shown in Figure 18) may be performed, for example, between step S2a, in which the first electrode 6a is formed on the support 10, and step S2b, in which the composite film 38 is attached to the support 10.

[0169] The quantum apparatus according to Embodiment 1 has a first electrode 6a positioned near the single-layer end 26. When a sufficiently large positive voltage is applied to this first electrode 6a, Cooper pairs are generated near the single-layer end 26. Therefore, the quantum apparatus according to Embodiment 1 makes it possible to inject Cooper pairs into the single-layer end 26 (i.e., the 2DTI end) without passing through a heterointerface.

[0170] The quantum apparatus according to Embodiment 1 further has a second electrode 6b positioned near the first electrode 6a and covering a portion of the single-layer end 26 in a plan view. Therefore, the quantum apparatus according to Embodiment 1 makes it possible to control the Fermi level in the portion of the single-layer end 26 that is close to the first electrode 6a (specifically, the third portion 12c).

[0171] The third section 12c (see Figure 4) is the region into which Cooper pairs, generated by the application of voltage to the first electrode 6a, penetrate. Controlling the Fermi level as described above is beneficial for extending the lifetime of Majorana quasiparticle pairs generated using topological superconductivity (see "(3) Operation").

[0172] (Embodiment 2) Embodiment 2 is similar to Embodiment 1. Therefore, the same parts as in Embodiment 1 will be omitted or simplified in their description.

[0173] (1) Structure Figure 34 is a plan view of an example of a quantum apparatus according to Embodiment 2. Figure 35 is a cross-sectional view of the quantum apparatus 202 shown in Figure 34 along a portion 46a of the XXXV-XXXV line. The cross-sectional view along another portion 46b of the XXXV-XXXV line is substantially the same as the cross-sectional view shown in Figure 34 and is therefore omitted.

[0174] The quantum device 202 illustrated in Figure 34 is obtained by adding first and second ferromagnetic materials 48a and 48b to the quantum device 2 shown in Figures 1-3. Quantum device 202 is a topological quantum device that produces Majorana quasiparticles.

[0175] The first ferromagnet 48a is positioned such that one of the Majorana quasiparticle pairs appears at a specific position P1 within the third portion 12c of the monolayer 4 while topological superconductivity is occurring in the third portion 12c of the monolayer 4. The second ferromagnet 48b is positioned such that the other of the Majorana quasiparticle pair appears at another specific position P2 within the third portion 12c of the monolayer 4 while topological superconductivity is occurring in the third portion 12c of the monolayer 4. The first and second ferromagnets 48a and 48b are, for example, cobalt or chromium.

[0176] The first and second ferromagnetic materials 48a and 48b are arranged between the support 10 and the first coating 8a (see Figures 34 and 35). Furthermore, in a plan view, the first ferromagnetic material 48a has an outer circumference surrounding one end of the third portion 12c of the single layer 4 (see Figure 34). On the other hand, the second ferromagnetic material 48b has an outer circumference surrounding the other end of the third portion 12c.

[0177] In this arrangement, one Majorana quasiparticle pair appears, for example, at a first position P1 within the third section 12c, which is closer to the first ferromagnet 48a than to the second ferromagnet 48b (see "(2) Operation"). The other Majorana quasiparticle pair appears, for example, at a second position P2 within the third section 12c, which is closer to the second ferromagnet 48b than to the first ferromagnet 48a. In other words, Majorana quasiparticle pairs appear at specific positions P1 and P2 within the third section 12c.

[0178] (2) Operation When a positive voltage is applied between the first electrode 6a and the third electrode 6c, Cooper pairs are generated in the first portion 12a of the single layer 4 (see Figure 4), and these Cooper pairs penetrate into the third portion 12c. As a result, topological superconductivity occurs in the third portion 12c (see "(3) Operation" in Embodiment 1).

[0179] The first ferromagnet 48a terminates this topological superconductivity at a first position P1 in its vicinity. Similarly, the second ferromagnet 48b terminates its topological superconductivity at a second position P2 in its vicinity. Then, Majorana quasiparticles (i.e., Majorana zero modes) appear at the first and second positions P1 and P2, respectively.

[0180] (3) Manufacturing method The quantum device 202 can be formed, for example, by adding a step of forming first and second ferromagnetic materials 48a and 48b on a support 10 (referred to as the fifth step S5 as appropriate) to the manufacturing method of the quantum device 2 (see Figure 1), which was described with reference to Figure 18. The first and second ferromagnetic materials 48a and 48b can be formed, for example, by lift-off of a ferromagnetic film.

[0181] The fifth step S5, which forms the first and second ferromagnetic materials 48a and 48b, is performed, for example, before step S2a (see Figure 18), which forms the first electrode 6a on the support 10, or between step S2b, which attaches the composite film 38 to the support 10, and step S2a.

[0182] (4) Variations Figure 36 is a plan view of another example of a quantum apparatus according to Embodiment 2 (hereinafter referred to as a modified example). Figure 37 is a cross-sectional view of the quantum apparatus 202m shown in Figure 36 along a portion 50a of the line XXXVII-XXXVII. The cross-sectional view along another portion 50b of the line XXXVII-XXXVII is substantially the same as the cross-sectional view shown in Figure 37 and is therefore omitted. The quantum apparatus 202m is similar to the quantum apparatus 2m1 according to Embodiment 1 (see Figure 24). Therefore, the parts common to quantum apparatus 2m1 are omitted from the explanation.

[0183] The modified quantum apparatus 202m is obtained by adding first and second ferromagnetic materials 48a and 48b, which are in contact with the support 10, to the quantum apparatus 2m1 shown in Figure 24. However, the second electrode 6b is a normal conductor.

[0184] As shown in Figure 37, the support 10, the first ferromagnetic material 48a, the second electrode 6b, the second coating 8b, the single layer 4, and the first coating 8a are arranged in this order. Similarly, the support 10, the second ferromagnetic material 48b, the second electrode 6b, the second coating 8b, the single layer 4, and the first coating 8a are arranged in this order.

[0185] Therefore, only the second coating 8b exists between the second electrode 6b and the single layer 4. As a result, the effect that the second electrode 6b exerts on the single layer 4 (i.e., the application of the second potential) is not hindered by the first and second ferromagnetic materials 48a and 48b.

[0186] A second electrode 6b exists between the first and second ferromagnetic materials 48a and 48b and the monolayer 4. However, since the second electrode 6b is a normal conductor, the magnetic field generated by the first and second ferromagnetic materials 48a and 48b is not disturbed by the second electrode 6b. Therefore, like quantum device 202, quantum device 202m can also generate Majorana quasiparticle pairs.

[0187] According to the modified version, the variations of the quantum device according to Embodiment 2 increase.

[0188] The quantum device 202m is obtained by adding first and second ferromagnetic materials 48a and 48b in contact with the support 10 to Modification 1 according to Embodiment 1 (i.e., quantum device 2m1). Similarly, the device obtained by adding a ferromagnetic material 48 in contact with the support 10 to Modification 2 according to Embodiment 1 is also an example of a quantum device according to Embodiment 2. The same applies to Modification 3 according to Embodiment 1.

[0189] The first and second ferromagnetic materials 48a and 48b may, instead of being in contact with the support 10, be in contact with a coating (for example, the first coating 8a of the quantum device 202m) located on the opposite side of the support 10, separated by a single layer 4 (see Figure 37).

[0190] The quantum device according to Embodiment 2 has a quantum device according to Embodiment 1 (i.e., a quantum device configured to cause topological superconductivity suitable for the generation of long-lived Majorana quasiparticle pairs). The quantum device according to Embodiment 2 further has first and second ferromagnetic materials 48a and 48b arranged so that Majorana quasiparticle pairs appear at specific locations within the region where topological superconductivity occurs. Therefore, according to the quantum device according to Embodiment 2, long-lived Majorana quasiparticle pairs can be generated at specific locations within the monolayer 4.

[0191] (Embodiment 3) Embodiment 3 has parts in common with Embodiments 1 and 2. Therefore, the parts in common with Embodiments 1 and 2 will be omitted or simplified in their explanation.

[0192] (1) Structure Figure 38 is a plan view of an example of a quantum apparatus according to Embodiment 3. Figure 39 is an enlarged view of the area 52 enclosed by the dashed line in Figure 38. Figure 38 shows the XL-XL line and the XLI-XLI line. These lines are bent in a crank shape midway through, as shown in Figure 39.

[0193] Figure 40 is a cross-sectional view along the XL-XL line shown in Figures 38 and 39. Figure 41 is a cross-sectional view along the XLI-XLI line shown in Figures 38 and 39.

[0194] The quantum device 302 shown in Figure 38 comprises a quantum device 202R according to Embodiment 2, a superconducting circuit 54, a microwave resonator 56, and a planar coil 57. The planar coil 57 may be omitted (see "(2) Method of Use and Operation").

[0195] Quantum device 202R is similar to quantum device 202 shown in Figure 34. However, the second coating 308b of quantum device 202R (see Figures 38, 40, and 41) differs from the second coating 8b shown in Figure 34 in that it has a pair of through holes 59a, 59b that reach the first portion 12a of the single layer 4 (see Figure 40). Otherwise, quantum device 202R and quantum device 202 shown in Figure 34 have substantially the same structure. In Figure 38, the symbols of several components common to quantum device 202R and quantum device 202 (e.g., the first to third electrodes 6a, 6b, 6c) are omitted.

[0196] The superconductor circuit 54 includes a first superconductor 58a (see Figure 40) in contact with the first portion 12a of the single layer 4, a second superconductor 58b (see Figure 41) in contact with the first portion 12a, and a third superconductor 58c (see Figures 38-41) that is different from the first and second superconductors.

[0197] The superconducting circuit 54 further has a first insulator 60a that covers the surface of the first superconductor 58a and has one end in contact with the third superconductor 58c (see Figures 38 and 40). The superconducting circuit 54 further has a second insulator 60b that covers the surface of the second superconductor 58b and has one end in contact with the third superconductor 58c (see Figures 38 and 41).

[0198] With these configurations, the superconductor circuit 54 has a first Josephson junction J1 that partially contains the first superconductor 58a, the first insulator 60a, and the third superconductor 58c, respectively (see Figures 38-40). The superconductor circuit 54 further has a second Josephson junction J2 that partially contains the second superconductor 58b, the second insulator 60b, and the third superconductor 58c, respectively, and is connected in parallel to the first Josephson junction J1 (see Figures 38, 39, and 41).

[0199] The first to third superconductors 58a, 58b, and 58c are, for example, aluminum. The first and second insulators 60a and 60b are, for example, aluminum oxide.

[0200] The microwave resonator 56 has a first transmission line 56a and a second transmission line 56b that is different from the first transmission line 56a (see Figure 38). A quantum device 202R and a superconducting circuit 54 are arranged between the first transmission line 56a and the second transmission line 56b.

[0201] The planar coil 57 is positioned so that the magnetic flux it generates penetrates the notch 62 (see Figure 39) between the first superconductor 58a and the second superconductor 58b. The microwave resonator 56 and the planar coil 57 are made of, for example, aluminum or niobium.

[0202] (2) How to use and operation Quantum device 302 is one of the minimum circuits (hereinafter referred to as Majorana minimum circuits) of a magnetic flux-controlled Majorana qubit (see, for example, Non-Patent Document 2). Quantum device 302 is configured such that superconductivity occurs in a portion of the single layer 4 (specifically, the first portion 12a). However, the quantum device according to Embodiment 3 may be configured such that topological superconductivity occurs in multiple portions of the single layer 4. Such a device (hereinafter referred to as a derivative circuit of quantum device 302) is also a Majorana minimum circuit.

[0203] A flux-controlled Majorana qubit can be formed by combining multiple Majorana minimal circuits (see, for example, Non-Patent Document 2). Therefore, a flux-controlled Majorana qubit (hereinafter referred to as a Majorana qubit according to Embodiment 3) can be formed by combining a derived circuit of the quantum device 302 with the quantum device 302.

[0204] A Majorana qubit according to Embodiment 3 is operated as follows: First, the Majorana qubit according to Embodiment 3 is cooled to near absolute zero. Next, multiple pairs of Majorana quasiparticles are generated by applying a voltage to the electrodes of each Majorana minimal circuit.

[0205] Due to the cooling described above, the first portion 12a, in which superconductivity is induced, integrates with the first and second superconductors 58a and 58b to form a single superconducting region. The same applies to the derived circuits of the quantum device 302. A "superconducting region" is a region that is in a superconducting state.

[0206] The processing up to this point activates the Majorana qubit according to Embodiment 3. After this, the quantum state rotation and quantum state reading of the Majorana qubit according to Embodiment 3 are performed.

[0207] The rotation of a quantum state can be achieved by controlling the parity of a Majorana quasiparticle pair (see, for example, Non-Patent Document 2). The parity of the Majorana quasiparticle pair changes depending on the intensity of the magnetic flux passing through the notch 62 (see Figure 39) of the superconductor circuit 54. Therefore, the quantum state is rotated by controlling the current flowing through the planar coil 57.

[0208] Alternatively, the magnetic flux passing through the notch 62 may be controlled by a coil placed near the quantum device 302 (for example, a coil placed directly above the notch 62). In this case, the quantum device 302 and its derived circuits do not need to have a planar coil 57.

[0209] The quantum state of the Majorana qubit according to Embodiment 3 can be read out, for example, by measuring the resonant frequency of the microwave resonator 56 (see, for example, Non-Patent Document 2).

[0210] (3) Manufacturing method Figure 42 is a process flow diagram showing an example of a manufacturing method for the quantum device 302. Figures 43 to 46 are cross-sectional process views along the XL-XL line shown in Figure 38. The cross-sectional process views along the XLI-XLI line are substantially the same as those shown in Figures 43 to 46 and are therefore omitted.

[0211] (3-1) Process 1 S1 to Process 5 S5 (See Figure 42) First, a quantum apparatus 202 according to Embodiment 2 is formed according to the first to fifth steps described in Embodiments 1 and 2 (see Figure 43).

[0212] (3-2) Sixth step S6 (see Figure 42) Next, through holes 59a and 59b (see Figure 44) that reach the first portion 12a of the single layer 4 are formed in the second coating 8b (see Figure 43).

[0213] Specifically, first, a photoresist film having a pair of openings above the first portion 12a is formed on the second coating 8b and the support 10. Then, the second coating 8b is etched through these openings by reactive ion etching until the first portion 12a is exposed. This etching forms a second coating 308b (see Figure 44) having through holes 59a and 59b. The through hole 59b (see Figure 38) is not shown in Figure 44 (and so on).

[0214] (3-3) Step 7 S7 (See Figure 42) Next, a superconducting circuit 54 is formed in contact with the first portion 12a (see Figure 45).

[0215] Specifically, first, a two-layer resist film having a cross-linked structure is formed. This two-layer resist film has a lower layer that is in contact with the support 10 (see Figure 44) and the second coating 308b, and an upper layer supported by the lower layer. The upper layer has a portion that protrudes from the lower layer (a so-called overhang) and an opening surrounded by this portion (hereinafter referred to as a resist opening).

[0216] This resist opening has an opening having substantially the same planar shape as the first superconductor 58a (hereinafter referred to as the first resist opening) and an opening having substantially the same planar shape as the second superconductor 58b (hereinafter referred to as the second resist opening). The resist opening further has an opening having substantially the same planar shape as the third superconductor 58c (hereinafter referred to as the third resist opening).

[0217] Next, the support 10 on which the two-layer resist film is formed is mounted in a vacuum deposition apparatus. Subsequently, a superconductor (for example, aluminum) is deposited onto the support 10 and the second coating 308b through the resist openings in the two-layer resist film.

[0218] This deposition process forms the first and second superconductors 58a and 58b. The deposition of the first and second superconductors 58a and 58b is carried out by oblique deposition. Oblique deposition is a technique for forming a thin film by using material vapor incident at an oblique angle onto a substrate (e.g., support 10).

[0219] The first and second superconductors 58a and 58b are formed by material vapor (e.g., aluminum vapor) incident on the support 10 through the first and second resist openings. Meanwhile, a thin film (not shown) having substantially the same planar shape as the third superconductor 58c is formed by material vapor incident on the support 10 through the third resist opening. This thin film is not included in the superconductor circuit 54.

[0220] Next, oxygen is introduced into the vacuum deposition apparatus in which the first and second superconductors 58a and 58b are formed. This forms a first insulator 60a (i.e., aluminum oxide) covering the surface of the first superconductor 58a and a second insulator 60b (i.e., aluminum oxide) covering the surface of the second superconductor 58b.

[0221] Next, oxygen is evacuated from the vacuum deposition apparatus. Then, the support 10 is rotated 180°. This rotation changes the angle of incidence of the material vapor. Finally, a superconductor (e.g., aluminum) is deposited onto the support 10 through the resist opening.

[0222] This deposition process forms a third superconductor 58c. The third superconductor 58c is obtained by material vapor incident on the support 10 through the third resist opening. Meanwhile, material vapor incident on the support 10 through the first and second resist openings forms thin films (not shown) having substantially the same planar shape as the first and second superconductors 58a and 58b. These thin films are not included in the superconductor circuit 54.

[0223] (3-4) Step 8 S8 (See Figure 42) Finally, a microwave resonator 56 having first and second transmission lines 56a and 56b, and a planar coil 57 are formed on the support 10 by lift-off of a superconducting film (e.g., an aluminum film) (see Figures 38 and 46).

[0224] (4) Variations Figures 47 and 48 show cross-sections of another example of a quantum apparatus according to Embodiment 3 (hereinafter referred to as a modified example).

[0225] The plan views of quantum apparatus 302m shown in Figures 47 and 48 are substantially the same as the plan view of quantum apparatus 302 (see Figure 38). In the following description, Figure 38 will be used as the plan view of quantum apparatus 302m. Figure 47 is a cross-sectional view along the line XL-XL in Figure 38. Figure 48 is a cross-sectional view along the line XLI-XLI in Figure 38.

[0226] The first superconductor 358a of quantum device 302m has a first region 364a separated from the first portion 12a of the monolayer 4, and a second region 364b in contact with both the first region 364a and the first portion 12a (see Figure 47). For example, aluminum is placed in the first region 364a. A superconductor having palladium atoms, tungsten atoms, and tellurium atoms is placed in the second region 364b. On the other hand, the first superconductor 58a of quantum device 302 (see Figure 40) is a single material (for example, aluminum).

[0227] Similarly, the second superconductor 358b of quantum device 302m has a third region 364c separated from the first portion 12a of the monolayer 4, and a fourth region 364d in contact with both the third region 364c and the first portion 12a (see Figure 48). For example, aluminum is placed in the third region 364c. A superconductor having palladium atoms, tungsten atoms, and tellurium atoms is placed in the fourth region 364d. On the other hand, the second superconductor 58b of quantum device 302 (see Figure 41) is made of a single material (for example, aluminum).

[0228] Aside from these, quantum device 302m and quantum device 302 shown in Figure 38 have substantially the same structure. The second range 364b and the fourth range 364d are superconductors obtained by diffusing palladium atoms into a single layer 4.

[0229] A superconductor is a material in which superconductivity occurs. Therefore, the first superconductor 358a, which has a range of compositions that differ from each other, is also a superconductor. The same applies to the second superconductor 358b.

[0230] The quantum device 302m can be formed, for example, by adding a step to form the second and fourth ranges 364b and 364d to the manufacturing method of the quantum device 302 shown in Figure 42. Specifically, at the beginning of step 7 S7, which forms the superconducting circuit 54, a thin layer of palladium is formed in the through holes 59a and 59b. The thin layer of palladium is formed, for example, by lift-off of the palladium film. Next, this thin layer and the single layer 4 are heated to cause a reaction between the thin layer and the single layer 4. As a result, the second and fourth ranges 364b and 364d are obtained. After that, the process described with reference to Figures 44 and 45 is continued.

[0231] According to this manufacturing method, a clean interface can be formed between the second range 364b of the first superconductor 358a and the single layer 4, thereby improving the contact resistance between the first superconductor 358a and the single layer 4. The same applies to the contact resistance between the second superconductor 358b and the single layer 4.

[0232] The quantum device according to Embodiment 3 is a Majorana minimal circuit (i.e., the smallest unit of a flux-controlled Majorana qubit) having the quantum device according to Embodiment 2. The quantum device according to Embodiment 2 can generate long-lived Majorana quasiparticle pairs. Therefore, the quantum device according to Embodiment 3 can construct qubits that perform quantum operations based on long-lived Majorana quasiparticle pairs.

[0233] As described above, the embodiments of the present invention have been explained. However, Embodiments 1 to 3 are illustrative and not restrictive. For example, the first and second films 8a and 8b illustrated in Embodiments 1 to 3 are hexagonal boron nitride. However, one or both of the first and second films 8a and 8b according to Embodiments 1 to 3 may be a substance different from hexagonal boron nitride (for example, any one of graphene, SiO2, SiN, alumina, amorphous boron nitride). However, when a substance different from the layer material (such as SiO2) is used as the film, it is preferable to attach a composite film having the film of the layer material and the single layer 4 to the film formed on the substrate by a stamp method.

[0234] The first electrode 6a illustrated in Embodiments 1 to 3 is separated from the single-layer outer periphery 16 (see FIG. 5) in plan view. However, the first electrode 6a may cover a part of the single-layer outer periphery 16 as long as it is separated from a certain range 14 of the single-layer outer periphery 16 in plan view.

[0235] The quantum device illustrated in Embodiments 1 to 3 has a third electrode 6c. However, the third electrode 6c may be omitted. In this case, for example, a first voltage is applied between the silicon substrate 11 and the first electrode 6a, and a second voltage is applied between the silicon substrate 11 and the second electrode 6b.

[0236] The quantum device according to Embodiment 3 has a first superconductor 58a and a second superconductor 58b different from the first superconductor 58a (see FIGS. 40 and 41). However, the second superconductor 58b may be the same superconductor as the first superconductor 58a. For example, the first superconductor 58a and the second superconductor 58b may be a U-shaped single superconductor coupled above the first portion 12a of the single layer 4. In this case, the quantum device according to Embodiment 3 may have one through hole 59a instead of the first and second through holes 59a and 59b (see FIG. 38).

[0237] The quantum apparatus according to Embodiments 2-3 has first and second ferromagnetic materials. However, the quantum apparatus according to Embodiments 2-3 may have electrodes that apply an electric field to both ends of a certain range 14 of the single-layer end 26 instead of the first and second ferromagnetic materials. Topological superconductivity can also be terminated by applying an electric field.

[0238] The first Josephson junction J1 according to Embodiment 3 (see Figures 39 and 40) has a first insulator 60a sandwiched between a first superconductor 58a and a third superconductor 58c. However, the first Josephson junction J1 may have a thin film of a normal conductor (e.g., palladium) instead of the first insulator 60a. The same applies to the second Josephson junction J2. In this case, the first and second superconductors 58a and 58b may be superconductors other than aluminum (e.g., niobium).

[0239] In the manufacturing method according to Embodiments 1 to 3, the single layer 4 separated from the 1T'-WTe2 single crystal is placed in a glove box filled with inert gas until the first step S1, in which the single layer 4 is sealed with the first and second coatings, is completed. However, the single layer 4 separated from the 1T'-WTe2 single crystal may be placed in an apparatus where the atmosphere has been exhausted, rather than in the glove box, until the first step S1 is completed.

[0240] The quantum apparatus illustrated in Figure 1, etc., has one first electrode 6a and one second electrode 6b. However, the quantum apparatus according to Embodiments 1 to 3 may have multiple first electrodes 6a and multiple second electrodes 6b so that topological superconductivity can be induced in multiple parts within the single layer 4. This quantum apparatus is an example of a derived circuit of the quantum apparatus 302 described above.

[0241] The following additional information is disclosed regarding the above embodiments 1 to 3.

[0242] (Note 1) A monolayer of tungsten ditelluride having a 1T'-type crystal structure, A first electrode that applies a first potential to a part of the single layer, which is separated from the outer circumference of the single layer, A second electrode, which is different from the first electrode, has a second electrode that applies a second potential to a part of the single layer and includes a certain range of the outer circumference, The first electrode is positioned so that Cooper pairs generated by the application of the first potential to the first portion can penetrate a third portion which is a part of the second portion and includes the certain range. The third portion is the region where topological superconductivity occurs when the Cooper pair penetrates. A quantum device characterized by its features.

[0243] (Note 2) The first electrode provides the first potential at which the Cooper pair is generated to the first portion. The second electrode provides the second potential, which is lower than the first potential, to the second portion. The quantum device described in Appendix 1 as a key feature.

[0244] (Note 3) The first electrode has a first outer circumference that is separated from the certain range in a plan view and surrounds the first portion of the single layer in a plan view. The second electrode, in a plan view, has a second outer circumference surrounding the second portion of the single layer, The aforementioned certain range extends along the first electrode in a plan view, The shortest distance between the first electrode and the certain range is the shortest distance between the outer circumference of the single layer and the first electrode. A quantum device characterized by the features described in Appendix 1 or 2.

[0245] (Note 4) Furthermore, a first coating is provided, with a portion of it positioned between the first electrode and the single layer. The invention has a second coating in which a portion is disposed between the second electrode and the single layer. A quantum device characterized by the features described in Appendix 1 or 2.

[0246] (Note 5) The second coating is the same coating as the first coating. The quantum device according to appended note 4, characterized in that...

[0247] (Appended note 6) Furthermore, it has a third electrode connected to a part of the single layer, which is different from the first part and the second part, The first potential is provided by the voltage applied between the first electrode and the third electrode, The second potential is provided by the voltage applied between the second electrode and the third electrode, The quantum device according to appended note 1 or 2, characterized in that...

[0248] (Appended note 7) The single layer is a single layer obtained from a single crystal of tungsten ditelluride having a 1T'-type crystal structure, The quantum device according to appended note 1 or 2, characterized in that...

[0249] (Appended note 8) Furthermore, while the topological superconductivity is occurring, a first ferromagnetic body arranged such that one of the Majorana quasiparticle pairs appears at a specific position within the third part, And a second ferromagnetic body arranged such that the other of the Majorana quasiparticle pairs appears at another specific position within the third part while the topological superconductivity is occurring, The quantum device according to appended note 1 or 2, characterized in that...

[0250] (Appended note 9) Furthermore, a first superconductor in contact with the first part, a second superconductor in contact with the first part, a third superconductor different from the first superconductor and the second superconductor, a first Josephson junction partially including each of the first superconductor and the third superconductor, and a second Josephson junction partially including each of the second superconductor and the third superconductor and connected in parallel to the first Josephson junction, a superconductor circuit having... A microwave resonator having a first transmission line and a second transmission line different from the first transmission line, The superconducting circuit and the single layer are arranged between the first transmission line and the second transmission line. The quantum device described in Appendix 8 as a key feature.

[0251] (Note 10) A first step involves covering the first surface of a single layer separated from a single crystal of tungsten ditelluride having a 1T'-type crystal structure with a first coating, and further covering the second surface of the single layer with a second coating. A second step of obtaining a first electrode that contacts the first coating, The process includes a third step of obtaining a second electrode that contacts the second coating, The second step is to obtain the first electrode such that, in a plan view, the first electrode is separated from a certain range of the outer circumference of the single layer, and in a plan view, the first outer circumference of the first electrode surrounds a portion of the single layer. Furthermore, the third step is to obtain the second electrode such that, in a plan view, the second outer circumference of the second electrode surrounds a certain range. The single layer is separated from the single crystal in a space where the atmosphere is removed, and thereafter is placed in a space where the atmosphere is removed until the first step is completed. A method for manufacturing a quantum device that is a key feature.

[0252] (Note 11) Furthermore, the method includes a fourth step of obtaining a third electrode, which is different from the first and second electrodes and is in contact with a portion of the single layer. A method for manufacturing the quantum device described in Appendix 10, which is a key feature.

[0253] (Note 12) The second surface is the same surface as the first surface. The second coating is the same coating as the first coating. A method for manufacturing a quantum device as described in Appendix 10 or 11.

[0254] (Note 13) The second step is to attach the first coating to the support on which the first electrode is formed, or to form the first electrode on the first coating. The third step is a step of forming the second electrode on the second coating, or a step of attaching the second coating to the support on which the second electrode is formed. A method for manufacturing a quantum device as described in Appendix 10 or 11. [Explanation of Symbols]

[0255] 2:Quantum device 4: Single layer 6a: 1st electrode 6b: 2nd electrode 6c: 3rd electrode 8a: 1st coating 8b: Second coating 10:Support 12a: 1st part 12b :Second part 12c: 3rd part 48a: First ferromagnetic material 48b: Second ferromagnetic material 54: Superconductor Circuits 56: Microwave resonator 56a: First transmission line 56b: Second transmission line 58a: First superconductor 58b: Second superconductor 58c: Third superconductor J1: First Josephson junction J2: Second Josephson junction

Claims

1. A monolayer of tungsten ditelluride having a 1T' type crystal structure, A first electrode that applies a first potential to a part of the single layer, which is separated from the outer periphery of the single layer, The present invention provides a second electrode, which is different from the first electrode, and which applies a second potential to a second portion of the single layer that includes a certain range of the outer circumference, The first electrode is positioned so that Cooper pairs generated by the application of the first potential to the first portion can penetrate a third portion which is a part of the second portion and includes the certain range. The third portion is the region where topological superconductivity occurs when the Cooper pair penetrates. A quantum device characterized by its features.

2. The first electrode provides the first potential at which the generation of the Cooper pair occurs to the first portion. The second electrode provides the second potential, which is lower than the first potential, to the second portion. The quantum apparatus as described in claim 1, characterized by its features.

3. The first electrode has a first outer circumference that is separated from the certain range in a plan view and surrounds the first portion of the single layer in a plan view. The second electrode, in a plan view, has a second outer circumference surrounding the second portion of the single layer, The aforementioned certain range extends along the first electrode in a plan view, The shortest distance between the first electrode and the certain range is the shortest distance between the outer circumference of the single layer and the first electrode. A quantum apparatus characterized by the features of claim 1 or 2.

4. Furthermore, a first coating is provided, with a portion of it positioned between the first electrode and the single layer. The invention has a second coating in which a portion is disposed between the second electrode and the single layer. A quantum apparatus characterized by the features of claim 1 or 2.

5. The second coating is the same coating as the first coating. The quantum apparatus as described in claim 4, characterized by its features.

6. Furthermore, it has a third electrode connected to a portion of the single layer that is different from the first and second portions, The first potential is given by the voltage applied between the first electrode and the third electrode. The second potential is given by the voltage applied between the second electrode and the third electrode. A quantum apparatus characterized by the features of claim 1 or 2.

7. The aforementioned monolayer is obtained from a single crystal of tungsten ditelluride having a 1T' type crystal structure. A quantum apparatus characterized by the features of claim 1 or 2.

8. Furthermore, a first ferromagnetic material is provided, which is arranged such that one of the Majorana quasiparticle pairs appears at a specific location within the third portion while the topological superconductivity is occurring. The system comprises a second ferromagnetic material in which, while the topological superconductivity is occurring, the other half of the Majorana quasiparticle pair appears at another specific location within the third portion. A quantum apparatus characterized by the features of claim 1 or 2.

9. Furthermore, a superconducting circuit having a first superconductor in contact with the first portion, a second superconductor in contact with the first portion, a third superconductor different from the first and second superconductors, a first Josephson junction partially containing the first and third superconductors, and a second Josephson junction partially containing the second and third superconductors and connected in parallel to the first Josephson junction, The microwave resonator has a first transmission line and a second transmission line different from the first transmission line. The superconducting circuit and the single layer are arranged between the first transmission line and the second transmission line. The quantum apparatus as described in claim 8, characterized by its features.

10. A first step involves covering the first surface of a single layer separated from a single crystal of tungsten ditelluride having a 1T'-type crystal structure with a first coating, and further covering the second surface of the single layer with a second coating. A second step of obtaining a first electrode that contacts the first coating, The process includes a third step of obtaining a second electrode that contacts the second coating, The second step is to obtain the first electrode such that, in a plan view, the first electrode is separated from a certain range of the outer circumference of the single layer, and in a plan view, the first outer circumference of the first electrode surrounds a portion of the single layer. Furthermore, the third step is to obtain the second electrode such that, in a plan view, the second outer circumference of the second electrode surrounds a certain range. The single layer is separated from the single crystal in a space where the atmosphere is removed, and thereafter is placed in a space where the atmosphere is removed until the first step is completed. A method for manufacturing a quantum device that is characterized by its features.

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