A method for large-scale production of quantum spin Hall edge states

Abstract

The present invention provides a method for mass-producing quantum spin Hall (QSH) edge states: by constructing an anisotropic surface topography of a topological material, modulating the Dirac cone of the surface energy band to form a quasi-one-dimensional band, i.e., a Q1D band, thereby generating a high density of QSH edge states. The present invention uses the topological material ZrTe<subgt;5< / subgt; for structural simulation. Its side surface has a large number of one-dimensional groove-like structures, and its edge states exhibit a Q1D band at the center of the Brillouin zone, thereby realizing a high density of QSH edge states. This invention provides a new idea for how to achieve a high density of QSH edge states, and promotes the development of the field of the development and application of electron spin devices based on topological insulating materials.

Description

Technical Field

[0001] The present invention belongs to the fields of spintronics and spintronic devices, and particularly relates to a method for realizing high-density QSH edge states in 3D topological materials. Background Art

[0002] The quantum spin Hall (QSH) state is a dissipationless edge state in a quantum spin Hall insulator or a two-dimensional (2D) topological insulator (TI). The carrier conductivity in the QSH state is not affected by the geometric structure of the boundary and has time-reversal invariance. These characteristics endow QSH insulators with great potential in the application development of spin quantum computing. Currently, the only possible scattering is backscattering. The spins of the conducting electrons in the QSH state can be flipped by magnetic defects. Currently, both theory and experiments have proven that the QSH state can be observed in HgTe / CdTe quantum wells, which has also been a research hotspot in recent years. Since there are only two QSH states with different propagation directions formed by different spins on each boundary, the dissipationless conducting channels are very limited.

[0003] To increase the conduction power, it is necessary to increase the density of the QSH state. A feasible method is to add more boundaries. One can increase the number of conducting channels by increasing the number of layers of the QSH insulator, and at the same time, weak interlayer interaction is required. 3D weak topological insulators (WTIs) can be formed by stacking 2D TIs. Due to the interlayer coupling, the side surfaces become anisotropic. However, as long as the interlayer interaction is weak enough, that is, the interlayer distance can be increased, the topological surface states will degenerate on the side surfaces and form independent edge states similar to those of a single layer, thus achieving a high density of topological edge states.

[0004] The ZrTe5 crystal material has characteristics of 3D quantum Hall effect. The ZrTe5 crystal will undergo a transition between 3D strong TI and weak TI as the lattice vector length changes. It has been theoretically proven that ZrTe5 is a 2D TI in the single-layer case and has a relatively large bandgap. Scanning tunneling microscopy / spectroscopy (STM / STS) experiments show that there are edge states at the step boundaries on the natural cleavage plane (010) of bulk single-crystal ZrTe5. However, due to the small number of surface step boundaries and the too weak boundary strength, they cannot be observed by ARPES, and it is difficult to confirm the energy band dispersion and non-trivial properties of the edge states. In short, for the ZrTe5 crystal material, there is currently no direct evidence of topologically QSH-like edge states measured by ARPES spectroscopy experiments. Summary of the Invention

[0005] Based on the above existing technologies, the present invention intends to design a method for large-scale fabrication of quantum spin edge states through existing theoretical assumptions and computational simulation means. The present invention uses ZrTe5 as the material to construct an anisotropic surface and produce a novel quantum spin device with high-density QSH edge states.

[0006] To achieve the invention objective of mass-producing quantum spin boundary states, the technical solution provided by the present invention is as follows: constructing an anisotropic surface topography using topological materials, and modulating the Dirac cone of the surface energy band to generate a quasi-one-dimensional band (Q1D) to achieve high-density QSH boundary states. Specifically, the present invention selects the topological material ZrTe5 as the model construction material, cuts ZrTe5 from the side to construct an anisotropic surface with multiple 1D grooves, generating a Q1D band. This surface is composed of the interlaced boundaries between vdW layers, making the QSH-like boundary states dense enough to form high-density QSH boundary states. And in the present invention, the high-density QSH boundary states can be directly observed and confirmed by ARPES.

[0007] The inventor proposed the above technical solution based on the following ideas. The inventor's calculations show that the flat boundary between adjacent vdW layers in the ZrTe5 crystal material is not the state with the lowest energy, but rather the uneven side surface has lower energy. Based on this characteristic, the inventor believes that the topography after peeling the side surface is likely to be uneven and will generate one-dimensional grooves; in this way, after peeling the side surface, QSH boundary states are generated along with multiple weakly coupled boundary grooves. At the same time, a clear linear dispersion and non-trivial quasi-one-dimensional band (Q1D) can be obtained by measuring the peeled side surface of ZrTe5 by ARPES, and this measurement result is highly consistent with the calculation result of the QSH boundary state of monolayer ZrTe5, which can also illustrate that the coupling between each boundary is very weak. That is to say, by artificially constructing a one-dimensional topography on the surface, a large number of QSH boundary states can be generated in a limited space, and this high-density QSH boundary state in the topological system will essentially improve the dissipationless conductive channels and has important potential value for the development of spintronic devices.

[0008] Specifically, the process of mass-producing spin Hall boundary states of the present invention is described as follows.

[0009] The present invention uses the ZrTe5 crystal material as the topological material for the construction model. The ZrTe5 crystal is a van der Waals (vdW) layered material with three-dimensional (3D) quantum Hall effect characteristics, and with the change of the lattice vector length, the transition between 3D strong TI and weak TI will occur.

[0010] First, in step one, the inventor calculates after obtaining and optimizing the lattice constants of ZrTe5. The obtained lattice constants of ZrTe5 are a = 3.975 Å, b = 14.311 Å, c = 13.572 Å, and the ZrTe5 crystal is a vdW layered structure.

[0011] Step 2: Perform calculations of the electron localization function (ELF) and projected crystal orbital Hamiltonian population (pCOHP) on the ZrTe5 obtained in step 1) to determine the bond-breaking mode of the Te atomic chain.

[0012] The natural dissociation plane of the ZrTe5 crystal material is the (010) plane. For monolayer ZrTe5, the Q1D ZrTe5 is stacked along the c-axis in a zigzag Te atomic chain. That is to say, in addition to being able to be exfoliated along the van der Waals (vdW) plane (i.e., the a-c plane), the a-b plane can also be used as an exfoliation plane. Therefore, a question will arise here, that is, when the a-b plane is used as the exfoliation plane, where is the chemical bond broken and what is the exfoliated surface morphology.

[0013] By calculating the detailed performance of the valence bond splitting after exfoliation along the a-b plane, the inventors found that the Zr-Te bond will break rather than the Te-Te bond during exfoliation, which is somewhat different from the assumptions of some previous theoretical works. Experimentally, the Q1D band formed on the side surface has been measured, and its spin, orbit, and partially unoccupied states have been obtained through ARPES measurement, proving its topologically non-trivial nature. Different from the previous calculation work on the a-b plane, the Q1D band is consistent with the boundary state of the monolayer, experimentally proving that monolayer ZrTe5 is indeed a 2D TI.

[0014] To further clarify its physical nature, the ELF of ZreTe5 was calculated to visualize this electron pairing situation. It was found that the electron overlap between Te atoms is greater than that between Zr and Te atoms. The 2D cross-section more intuitively shows that the Te-Te bond is stronger, which is consistent with the formation process of the ZrTe5 structure (inserting the ZrTe3 crystal into the Te-Te chain). pCOHP can also be used to characterize the strength of the bond. As expected, the pCOHP of both the bulk structure and the monolayer structure of ZrTe5 simultaneously proves that the Zr-Te bond is weaker than the Te-Te bond.

[0015] Therefore, there are two ways to break the chemical bond of the Te atomic chain of ZrTe5 obtained in step 2), one is the breaking of the Zr-Te bond, and the other is the breaking of the Te-Te bond.

[0016] Step 3: Construct the surface of the ZrTe5 obtained in step 1), consider the possible types of its side surface morphologies, determine the most likely surface morphology. In this step, there are mainly two types of side surface morphology configurations of ZrTe5, one is a flat surface, and the other is an uneven surface with multiple 1D grooves. Specifically as follows.

[0017] After determining the strength relationship between Zr-Te bonds and Te-Te bonds, there are two configuration cases between adjacent layers on the a-b surface after exfoliation. One is a flat surface, and the other is uneven. It is generally believed that the exfoliated surface is flat, and the terminal heights of each vdW layer are the same. However, the results of pCOHP show that it is antibonding near the Fermi level, indicating that the electrons between adjacent boundaries are unpaired in this case, that is, the electrons at adjacent terminals repel each other when the surface is flat. In the other case, that is, when the surface is uneven, this repulsive phenomenon disappears. The pCOHP is used to analyze the interaction between the nearest-neighbor Te-Te atoms under these two surfaces. It can be obtained from the pCOHP that the Te-Te bonding strength under the stepped boundary is stronger than that under the flat surface of the boundary. This result indicates that the ab exfoliated surface of ZrTe5 is likely not a flat surface, but a rough surface with vdW terminals or a surface with various step heights, that is, an uneven surface containing multiple 1D grooves, which is an anisotropic surface.

[0018] Step 4: Perform band calculations on the surface with the lateral surface morphology configuration of ZrTe5 obtained in Step 3 to study its band performance characteristics. Specifically as follows.

[0019] The calculated simulation configuration of the uneven surface with multiple 1D grooves has a length of 7 unit cell c-axes along the c-axis, with a total of 14 Zr atomic layers. The adjacent two vdW layers are staggered to form two symmetric upper and lower surfaces, and the staggered length is 3 unit cell c-axes. The vacuum layer is greater than 15 Å. The lattice constants of this simulation structure are a = 7.426 Å and b = 13.572 Å. Calculating the band of ZrTe5 with an uneven vdW boundary surface shows that there is a Dirac cone near the Fermi level in the band gap, and there is no scattering along the vdW direction, forming a Q1D band. This topological non-trivial state is similar to the QSH state when calculating monolayer ZrTe5, indicating that the interlayer coupling is extremely weak when the surface morphology is uneven. This is further confirmed by calculating the real-space distribution of the boundary state. If the vdW boundaries are all decoupled, then a high-density QSH state will appear, and a large number of QSH channels will be generated. There are many stepped structures on the a-b surface after surface exfoliation observed by scanning electron microscopy, which is consistent with the theoretical prediction. It shows that constructing weak-coupling boundaries on the surface or in the body to obtain high-density QSH channels is a general method.

[0020] However, the existence of this high-density QSH state on the surface still needs to be proved by APRES experiments, especially the topological non-trivial characteristics of the state.

[0021] To prove the existence of high-density QSH edge states in ZrTe5, the band structure of the ab exfoliated surface was experimentally studied, with light waves of various energy ranges and polarizations incident. As expected, the a-b plane has sufficient intensity to be observed by ARPES, and the Q1D bands can be clearly seen on the conventionally exfoliated vdW surface. When the a-b surface is irradiated with 25 eV polarized light, the bands of ZrTe5 near the Fermi energy along the k a direction, two hole bands can be clearly resolved. When the energy of the incident light is changed to 89 eV, the shape of the lower hole band changes from "Λ" to "M", indicating that this is the bulk valence band. However, the scattering of the upper band remains, indicating that there is no scattering along the k z direction. The waterfall plot of the energy dispersion curve (EDC) also shows the Q1D band characteristics.

[0022] Two types of terminations were considered in the calculation. Although the Te-Te bond is stronger than the Zr-Te bond, the cases of breaking the Te-Te bond and the Zr-Te bond were calculated separately. When the Zr-Te bond is broken, there is a clearer linear scattering Dirac band at the Γ point of the Brillouin zone in the bulk band. On the contrary, when the Te-Te bond is broken, there is a more complex situation with band crossing at the X point. This is an important difference in the band structure and can be demonstrated by ARPES experiments. The experimental results are the same as those for the broken Zr-Te bond. Obviously, in the real situation, the Zr-Te bond is more likely to break. At the same time, the calculation results of this monolayer ZrTe5 are consistent with the experimental results of the a-b surface of bulk ZrTe5, proving that the 1D groove structure is not a surface state but more like a QSH edge state. Due to the small boundary-to-volume ratio, usually, edge states can hardly be observed by ARPES spectroscopy. However, as long as there are enough boundaries, such as the a-b surface here, the QSH of such intensity is sufficient to be observed by ARPES. In addition, topological edge states are observed in the bulk band, which directly proves that monolayer ZrTe5 is a 2D TI. The edge states found in ZrTe5 open up ideas for the development of spin devices, indicating that high-density QSH can be found in 2D / 3D topological systems as long as the 1D boundary coupling is weak.

[0023] Through the above method, the inventors obtained a model with high-density QSH boundary states. The material used to construct the model is the topological material ZrTe5. By cutting the ZrTe5 crystal material from the side, using the stacking direction of the zigzag Te atomic chain (i.e., the a-b plane) as the exfoliation plane, breaking at the Zr-Te bond, and constructing an anisotropic surface with multiple 1D grooves, the model of the QSH boundary state is formed. Further, the model is as follows: along the c-axis of the ZrTe5 crystal material, it is 7 unit cell c-axis lengths, with a total of 14 Zr atomic layers. The adjacent two vdW layers are staggered to form two symmetric upper and lower surfaces, and the staggering length is 3 unit cell c-axes, and the vacuum layer is greater than 15 Å. The structural lattice constants of the model are a = 7.426 Å and b = 13.572 Å.

[0024] In the above research and in the embodiments of the present invention, the inventors used the VASP software package for first-principles calculations and described the ion-electron interaction using the PAW method. The exchange functional was described using GGA-PBE. The cutoff energy of the plane wave was 500 eV. The energy convergence criterion was 1×10 -6 eV, and the force convergence criterion was 0.01 eV / Å. Spin-orbit coupling (SOC) was considered. To obtain the maximally localized Wannier functions (MLWFs) and topological states, the Wannier90 and WannierTools software packages were used. To simulate the 1D / 2D thin film structure, a vacuum layer greater than 15 Å was adopted. The k-points of the unit cell of ZrTe5, the 2D and 1D band systems were sampled in a Γ-centered manner of 9×9×5 and 15×5×1 and 15×1×1, respectively. pCOHP was used to describe the information of the bonds between atoms. Description of the Drawings

[0025] Figure 1 Schematic diagram of the method for the present invention to realize large-scale fabrication of quantum spin Hall boundary states

[0026] Figure 2 Two possible bond-breaking methods of ZrTe5 along the c-axis.

[0027] Figure 3 Two possible structures of the surface morphology of ZrTe5.

[0028] Figure 4 Energy bands of ZrTe5 under anisotropic surface morphology.

[0029] Figure 5 Projection of the charge distribution of the boundary state in real space under the anisotropic surface morphology of ZrTe5.

[0030] Figure 6 Energy bands of ZrTe5 under flat and uneven surface morphologies.

[0031] Figure 7 The energy bands of the a-b plane of ZrTe5 were measured experimentally. Specific implementation manners

[0032] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. However, it should be understood that these examples are only used to illustrate in more detail and should not be construed as limiting the present invention in any form.

[0033] The inventor proposed a method for fabricating quantum Hall edge states on a large scale, as Figure 1 is a schematic diagram of the method for fabricating quantum Hall edge states of the present invention. An anisotropic surface morphology is constructed using a topological material, and the Dirac cones of the surface energy bands are modulated to generate quasi-one-dimensional bands, realizing high-density QSH edge states.

[0034] In the following embodiments, an anisotropic surface was constructed using the topological material ZrTe5 through calculation and simulation methods, etc., to realize high-density QSH edge states. The specific operation embodiments are as follows.

[0035] Embodiment 1

[0036] (1) The topological material ZrTe5 was selected to construct an anisotropic surface, and the possible ways of chemical bond cleavage were studied. Specifically as follows.

[0037] The bulk ZrTe5 crystal material was used, which has the characteristics of 3D quantum Hall effect. The inventor obtained the lattice constants of ZrTe5 and performed calculations after optimization, obtaining the lattice constants of ZrTe5 as a = 3.975 Å, b = 14.311 Å, c = 13.572 Å. The ZrTe5 crystal is a vdW layered structure. As Figure 2 shows, it can be seen that in addition to the traditional vdW plane a-c plane that can be used as a peeling plane for ZrTe5, the stacking direction of the zigzag Te atomic chains (a-b plane) can also be used as a peeling plane. Considering the a-b plane as the surface after peeling, the cleavage position of the chemical bond needs to be considered. As Figure 2 shows two possible bond cleavage ways of ZrTe5 along the c-axis. The bond cleavage ways on the left and right are Zr-Te bond cleavage and Te-Te bond cleavage respectively. Usually, it would be considered that the Zr-Te bond is less likely to break. However, the ELF and pCOHP calculations based on the crystal structure of ZrTe5 in the present invention show that the Te-Te bond is stronger than the Zr-Te bond, and the Zr-Te bond is more likely to break.

[0038] After obtaining the most likely bond cleavage way, the possible surface morphologies were studied. Specifically as follows.

[0039] Based on the calculation results of step (1), the surface topography after peeling can be roughly divided into two types, as Figure 3 These are two possible structures of the ZrTe5 surface topography. In the left figure of the figure, it is a flat surface, and in the right figure, it is an uneven surface. Combining the pCOHP calculation results and analyzing the interaction between adjacent atoms, it can be seen that the side surface is more inclined to form an uneven surface, and this theoretical result has also been confirmed by experiments.

[0040] After obtaining the surface topography with the greatest possibility, study its energy band characteristics. Specifically as follows.

[0041] Based on the possible surface topographies in step (2), perform energy band calculations, as Figure 4 The energy bands under the anisotropic surface topography of ZrTe5 are shown. It is found that when an anisotropic surface topography is formed, a Q1D band is generated at the Γ point in the Brillouin zone. There is a Dirac cone near the Fermi level in the band gap, and there is no scattering along the vdW direction, forming a Q1D band. This topological non-trivial state is similar to the QSH state when calculating monolayer ZrTe5, indicating that the interlayer coupling is extremely weak when the surface topography is uneven, and this is further confirmed by calculating the real-space distribution of the edge states, specifically as Figure 5 The projection of the charge distribution of the edge states in real space under the anisotropic surface topography of ZrTe5 is shown.

[0042] In addition, the energy band diagrams under the flat surface are calculated. The two cases are as Figure 6 The energy bands under the flat and uneven surface topographies of ZrTe5 are shown respectively. Figure 7 This is the energy band of the a-b plane of ZrTe5 measured experimentally. By comparing the experimental results in this figure, it is further shown that the side surface is uneven, that is, anisotropic, in the real situation.

[0043] The above is a detailed description of the best embodiment of the present invention. However, obviously, researchers in the technical field of the present invention can make non-substantive changes in form and content according to the above steps without departing from the scope of the present invention's essential protection. Therefore, the present invention is not limited to the above specific forms and details.

Claims

1. A model with high-density QSH edge states, characterized in that: The construction material of the model is the topological material ZrTe5. By cutting the ZrTe5 crystal material from the side, with the stacking direction of the zigzag Te atomic chain, that is, the a-b plane, as the exfoliation plane, the Zr-Te bond is broken to form an anisotropic surface with multiple 1D grooves, constituting the model with high-density QSH boundary states; The model is: along the c-axis of the ZrTe5 crystal material, it is 7 unit cell c-axis lengths, and there are a total of 14 Zr The atomic layer, where the adjacent two vdW layers are staggered to form two symmetric upper and lower surfaces, the staggering length is 3 unit cell c-axes, and the vacuum layer is greater than The structural lattice constant of the said model is 2. A method for mass-producing quantum spin Hall edge states, characterized in that: Using the topological material to construct an anisotropic surface morphology, modulating the Dirac cone of the surface energy band to form a quasi-one-dimensional band, that is, the Q1D band, to achieve high-density QSH boundary states; The topological material is the ZrTe5 crystal material, which is a van der Waals layered material with three-dimensional quantum Hall effect characteristics. As the lattice vector length changes, the transition between 3D strong TI and weak TI will occur; The natural dissociation plane of the ZrTe5 crystal material is the a-c plane. For a single layer of ZrTe5, ZrTe5 is stacked along the c-axis zigzag Te atomic chain, and the a-b plane can be used as the exfoliation plane; The method of using the topological material to construct an anisotropic surface morphology and form a quasi-one-dimensional band includes the following steps: 1) Obtain the lattice constant of ZrTe5, optimize it, and then perform calculations; 2) Perform electron localization function and crystal orbital Hamiltonian population projection calculations on the ZrTe5 obtained in step 1) to determine the bond-breaking method of the chemical bond of the Te atomic chain; 3) Construct the exfoliation plane with the ZrTe5 parameters obtained in step 1). According to the possible types of the exfoliation plane morphology, use pCOHP to analyze the interaction between adjacent Te-Te atoms on the exfoliation plane to determine its exfoliation plane morphology; 4) Perform energy band calculations on the exfoliation plane obtained in step 3), and determine its calculation simulation configuration according to the characteristics of its energy band performance; Step 1) The obtained lattice constant of ZrTe5 is and the ZrTe5 crystal is a vdW layered structure; There are two ways to obtain the bond-breaking method of the chemical bond of the Te atomic chain in ZrTe5 in step 2), one is the Zr-Te bond breaking, and the other is the Te-Te bond breaking; There are two types of exfoliation plane morphology configurations of ZrTe5 in step 3): one is a flat surface, and the other is an uneven surface with multiple 1D grooves, that is, an anisotropic surface; In step 4), the computational simulation configuration is determined as follows: the computational simulation configuration of the uneven surface forming multiple 1D grooves is 7 unit cell c-axis lengths along the c-axis, with a total of 14 Zr atomic layers. The adjacent two vdW layers are staggered to form two symmetric upper and lower surfaces, and the staggered length is 3 unit cell c-axes. The vacuum layer is greater than and the structural lattice constant of the simulation configuration is

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