Method for regulating and controlling Rashba spin splitting in WSeTe single layer

Abstract

The embodiment of the invention discloses a method for regulating and controlling Rashba spin splitting in a WSeTe single layer, and the method comprises the steps: selecting single-layer WSeTe, and carrying out the structure optimization; determining a net intrinsic electric field direction through charge density difference and work function calculation; on the basis of energy band calculation containing / not containing spin orbit coupling, gamma point spin splitting is observed; verifying the characteristics of Rashba splitting according to the spin texture graph, and analyzing the main contribution of Rashba splitting according to the energy band projection graph; applying in-plane biaxial strain to regulate and control the Rashba splitting strength; applying a vertical electric field to regulate and control the Rashba splitting strength; and meanwhile, strain and an electric field are applied to regulate and control the Rashba splitting strength. In-plane biaxial strain and vertical electric field independent regulation and control and common regulation and control are selected, and the regulation and control means of Rashba spin splitting are added. By adopting the technical scheme of the invention, more effective strain electric field control is expected to be realized by reasonably designing the material symmetry and the energy band structure.

Description

Technical Field

[0001] This invention relates to the field of spintronic materials technology, and more particularly to a method for controlling Rashba spin splitting in WSeTe monolayers. Background Technology

[0002] Since the discovery of graphene in 2004, researchers have made significant progress in the structure of two-dimensional materials. The discovery of novel two-dimensional materials such as hexagonal boron nitride (h-BN), transition metal dichalcogenides (TMDs), and silicene has greatly expanded the physical significance and potential applications of low-dimensional quantum materials. Among them, monolayer TMDs (MX2, M = Mo / W; X = S / Se / Te) have important applications in optoelectronic devices and field-effect transistors due to their unique mechanical strength, tunable bandgap (1.1-1.9 eV), and spin-orbit coupling (SOC) effect.

[0003] The most prominent example is the Janus tmd (MXY, X≠Y) developed in recent years. Compared with the symmetric structure of traditional tmd, the inherent structural inversion asymmetry (SIA) of Janus materials enables them to generate a strong RashbaSOC effect near the Fermi surface.

[0004] Rashba spin splitting is crucial in spintronics because it allows manipulation of electron spin states using an external electric field rather than a magnetic field, which is highly attractive for low-power spin devices. External electric fields, strain, and charge doping can effectively control Rashba spin splitting in two-dimensional Janus tmd. However, the potential of utilizing both strain and electric fields to manipulate the spins together, and how to improve the tuning efficiency of Rashba spin splitting, has not yet been investigated.

[0005] The above problems urgently need to be solved. Summary of the Invention

[0006] To address the related technical problems, this invention provides a method for controlling Rashba spin splitting in a WSeTe monolayer, thereby resolving the issues mentioned in the background section above.

[0007] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0008] This invention provides a method for controlling Rashba spin splitting in a WSeTe monolayer, the method comprising:

[0009] A single-layer WSeTe was selected, and its structure was optimized.

[0010] The direction of the net intrinsic electric field was determined by calculating the charge density difference and work function.

[0011] Based on band structure calculations with / without spin-orbit coupling, spin splitting at the Γ point is observed;

[0012] The Rashba splitting characteristics were verified based on the spin texture map, and the main contributions of the Rashba splitting were analyzed based on the band projection map.

[0013] Applying in-plane biaxial strain modulates the Rashba splitting intensity;

[0014] Applying a vertical electric field modulates the Rashba splitting intensity;

[0015] Simultaneously apply strain and electric field to modulate the Rashba splitting intensity.

[0016] As an optional implementation, the single-layer WSeTe is a two-dimensional periodic structure.

[0017] As an optional implementation, the step of determining the direction of the net intrinsic electric field by calculating the charge density difference and work function includes:

[0018] The work function difference is determined based on the local potential energy of the Se atomic layer and the local potential energy of the Te atomic layer.

[0019] As an optional implementation, the observation of spin splitting at the Γ point based on band structure calculations with / without spin-orbit coupling includes:

[0020] The spin splitting phenomenon was observed by calculating the band structure with and without SOC.

[0021] As an optional implementation, the step of verifying Rashba splitting characteristics based on spin texture maps and analyzing the main contributions of Rashba splitting based on band projection maps includes:

[0022] In momentum space, the in-plane and out-of-plane spin components of the upper and lower bands are calculated to confirm the existence of Rashba spin splitting; the main contribution sources of Rashba spin splitting are analyzed based on the band projection diagram.

[0023] As an optional implementation, the application of in-plane biaxial strain to modulate the Rashba splitting intensity includes:

[0024] Rashba spin splitting increases with increasing compressive strength and decreases with increasing tensile strength; applying in-plane biaxial strain modulates the Rashba splitting intensity.

[0025] As an optional implementation, the application of a vertical electric field to modulate the Rashba splitting intensity includes:

[0026] When an electric field is applied, α RIt increases slightly with the increase of electric field strength, and its increase is one-third of that of strain operation.

[0027] As an optional implementation, the simultaneous application of strain and electric field to modulate the Rashba splitting intensity includes:

[0028] Biaxial strain directly regulates orbital overlap and hybrid orbital strength through changes in lattice constant; strain dominates under the joint regulation of Rashba spin splitting by the strain electric field.

[0029] The technical solution proposed in this invention selects in-plane biaxial strain, and separately and jointly controls the vertical electric field, increasing the means of controlling Rashba spin splitting. The manipulation mechanism disclosed in this invention provides a theoretical basis for its extension to other two-dimensional polar semiconductor structures. By adopting the technical solution of this invention and rationally designing material symmetry and band structure, more effective strain electric field manipulation is expected to be achieved, and it is expected to be applied to high-efficiency spintronic devices. Attached Figure Description

[0030] To more clearly illustrate and understand the technical solutions in the embodiments of the present invention, the accompanying drawings used in the background technology and embodiment descriptions of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the content of the embodiments of the present invention and these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the method for regulating Rashba spin splitting in a WSeTe monolayer provided in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of the WSeTe monolayer atomic structure, charge density difference, and work function provided in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of the single-layer WSeTe band structure and Γ-point spin polarization distribution provided in an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the WSeTe single-layer band projection provided in an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram of the WSeTe band structure under biaxial strain modulation provided in an embodiment of the present invention;

[0036] Figure 6 The strain / electric field pair α provided in the embodiments of the present invention R The influence of band gap, bond length and PDOS;

[0037] Figure 7 Provided for embodiments of the present invention Electric field + strain band structure (a), electric field / strain pair α R Schematic diagram of the control relationship (b) and the comparison of PDOS under -3% strain and superimposed electric field (c). Detailed Implementation

[0038] To make the technical problems solved by the present invention, the technical solutions adopted, and the technical effects achieved clearer, the technical solutions of the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Please refer to Figures 1 to 7 The specific details regarding the accompanying drawings are as follows: Figure 2 (a) Top view of the atomic structure of a WSeTe monolayer. (b) Charge density difference in WSeTe, with the electron depletion region in cyan and the electron accumulation region in yellow. In (a) and (b), the light green, gray, and dark green spheres represent Se, W, and Te atoms, respectively. (c) Work function of WSeTe. Z is the thickness of WSeTe, and the black arrow indicates the net intrinsic electric field. Figure 3 (a) Band structure without considering SOC. (b) Band structure considering SOC. (c) Schematic diagram of the first Brillouin zone of WSeTe, where b and b are reciprocal space vectors. (d) Enlarged view of the band structure of the highest valence band near the Γ point. (e) and (f) Spin polarization distribution near the Γ point: (e) Spin polarization vector of the lower band structure near the Γ point (S x ,S y (f) The spin polarization vector of the upper band structure near the Γ point (S) is indicated by a pink arrow. x ,S y (Indicated by blue arrows). The color scale on the right is used to quantitatively characterize the spin projection S. z .exist Figure 4 Projected band structure of (a) W atom, (b) Se atom, and (c) Te atom. Figure 5 The image shows the band structure of WSeTe under different in-plane biaxial strains of -3%, -2%, -1%, 0%, 1%, 2%, 3%, 4%, 5%, and 6%. The arrows indicate the band gaps. Figure 6 (a) α under different biaxial strains (pink circles) and applied electric fields (blue pentagrams) R(b) Band gaps under different biaxial strains. Pink squares represent indirect band gaps, and blue triangles represent direct band gaps. (c) Trends in W-Se, W-Te, and Se-Te bond lengths with strain (blue: W-Se, pink: W-Te, black: Se-Te). (d) PDOS of WSeTe under different biaxial strains of -2%, 0%, 2%, 4%, and 6%. Figure 7 (a) Band structure of monolayer WSeTe under strain of -2%, 0%, 2%, 4%, and 6% applied under an electric field of 0.4 V / A. (b) Effect of biaxial strain (pink squares) and pure strain (blue circles) of -2%, 0%, 2%, 4%, and 6% on αR under an electric field of 0.4 V / A. (c) PDOS with strain of -3% and strain of 0.4 V / A and strain of -3%.

[0040] As shown in the figure, the method 100 for controlling Rashba spin splitting in a WSeTe monolayer in this embodiment includes the following steps:

[0041] S101. Select a single-layer WSeTe and optimize its structure;

[0042] S102. The direction of the net intrinsic electric field is determined by calculating the charge density difference and work function.

[0043] S103. Based on band structure calculations with / without spin-orbit coupling, observe spin splitting at the Γ point;

[0044] S104. Verify the Rashba splitting characteristics based on the spin texture map, and analyze the main contributions of the Rashba splitting based on the band projection diagram;

[0045] S105. Apply in-plane biaxial strain to control the Rashba splitting intensity;

[0046] S106. Apply a vertical electric field to control the Rashba splitting intensity;

[0047] S107. Simultaneously apply strain and electric field to control the Rashba splitting intensity.

[0048] For example, in step S101, a suitable research structure, a single-layer WSeTe, is selected and structural optimization is performed. Preferably, the single-layer WSeTe is a two-dimensional periodic structure with a lattice constant of approximately [value missing].

[0049] For example, in step S102, the charge density difference and work function are calculated for the monolayer WSeTe to confirm the direction of the net intrinsic electric field. Based on the local potential energy of the Se atom layer and the local potential energy of the Te atom layer, the work function difference is determined. In this embodiment, the local potential energy of the Se atom layer is 0.925 eV higher than that of the Te atom layer, i.e., the work function difference ΔV = 0.925 eV. This potential gradient directly drives the strong net electric field from the Te layer to the Se layer. The formation mechanism of this potential gradient can be seen by calculating the charge density difference. Electron accumulation can be observed around both Se and Te atoms. Around the W atom, there is an electron loss. Further quantitative comparison shows that the electron accumulation intensity around the Se atom is greater than that around the Te atom, indicating that the Se atom has a greater ability to absorb electrons than the Te atom. Based on the correlation between charge distribution and the direction of the net electric field, it can be inferred that the net electric field points from the Te atom to the Se atom.

[0050] For example, step S103, based on band structure calculations with / without spin-orbit coupling, observes spin splitting at the Γ point, including: calculating and observing the spin splitting phenomenon using band structures with and without SOC. Due to the arrangement of Se and Te atoms in the WSeTe lattice, the original hexagonal crystal structure symmetry is broken, and the symmetry is reduced to triplet symmetry. In the Brillouin zone, the reduction in symmetry level directly changes the equivalence of high symmetry points (K and K′ points are no longer equivalent). Band structures with and without SOC are shown respectively. It can be seen that there is obvious spin splitting near the Γ point.

[0051] For example, in step S104, verifying the Rashba splitting characteristics based on the spin texture map and analyzing the main contributions of the Rashba splitting based on the band projection map includes: calculating the in-plane and out-of-plane spin components of the upper and lower branches of the band in momentum space to determine the existence of Rashba spin splitting; and analyzing the main sources of contribution of Rashba spin splitting based on the band projection map.

[0052] In momentum space, the spin directions of the two valence bands at point Γ are determined. Near point Γ, the upper band exhibits counterclockwise in-plane spin polarization, while the lower band exhibits clockwise in-plane spin polarization. For the upper and lower band branches, the in-plane and out-of-plane spin components also show opposite characteristics, confirming the existence of Rashba spin splitting. Subsequently, the focus shifts to determining the α at point Γ. R By measuring E R and k R The intensity of Rashba spin splitting can be obtained as follows:

[0053]

[0054] E R k R and αR 40,000 meV respectively and Rashba spin splitting originates from W's dz 2 The orbital and the pz orbital of Se.

[0055] For example, in step S105, applying in-plane biaxial strain to regulate the Rashba splitting intensity includes: Rashba spin splitting increases with increasing compressive strength and decreases with increasing tensile strength, and applying in-plane biaxial strain to regulate the Rashba splitting intensity.

[0056] Rashba spin splitting exhibits a significant response to biaxial strain. Rashba spin splitting increases with increasing compressive strength. Under tensile conditions, the Rashba spin splitting at point Γ gradually decreases with increasing tensile strain. The ideal maneuver point is at -2% strain, α R It reaches its maximum at -2% and decreases slightly at -3%. α R At -2% compression, the amplitude is increased by 57% compared to the uncompressed state. Conversely, this value decays due to tensile strain. At 6%, Rashba spin splitting practically disappears. Calculating the density of states projection plot for strain shows that tensile strain leads to a decrease in the electronic density of states of the Wd and Se / Te-p orbitals due to increased bond lengths and reduced orbital overlap. At larger tensile strains, the disappearance of orbital overlap ultimately leads to a decrease in the amplitude of Rashba spin splitting. Therefore, the overlap and hybridization strength of the Wd-Se-p orbitals determine Rashba spin splitting.

[0057] For example, in step S106, applying a vertical electric field to modulate the Rashba splitting intensity includes: when the electric field is applied, α R It increases slightly with the increase of electric field strength, and its increase is one-third of that of strain operation.

[0058] Specifically, when an electric field is applied, α R It increases slightly with increasing electric field strength, reaching its maximum at an electric field strength of... Time to reach Its increase is only one-third of that of strain operation (ε = -2%), indicating that the electric field's ability to manipulate Rashba spin splitting is relatively limited.

[0059] For example, in step S107, the simultaneous application of strain and electric field to regulate the Rashba splitting intensity includes: biaxial strain directly adjusts the orbital overlap and hybrid orbital intensity through changes in the lattice constant; strain dominates under the joint regulation of Rashba spin splitting by the strain electric field.

[0060] Specifically, biaxial strain directly modulates orbital overlap and hybrid orbital strength through changes in the lattice constant, significantly controlling the Rashba spin splitting intensity. Conversely, due to the strong shielding effect of two-dimensional materials, the manipulation efficiency of the vertical external electric field is constrained by the following dual limiting mechanisms. First, the external electric field has difficulty penetrating the anion layer to directly affect the cations, and the cations are insensitive to the electric field response, resulting in a geometric shielding effect. Second, the polarization electric field generated by the redistribution of charges in the plane is the source of the electrostatic shielding effect, thus reducing the manipulation effect of the external field on the electric dipole moment. On the other hand, through orbital modulation, strain engineering provides substantial benefits for directly controlling the Rashba spin splitting of the material. Therefore, it plays a prominent role in strain-electric field manipulation. When ε = -2% to 6%, the influence of the electric field on Rashba spin splitting is dominant under the action of the strain electric field, but when ε = -3%, the influence of the electric field on Rashba spin splitting becomes more significant. According to the PDOS distribution of the superimposed electric field and pure strain under strain conditions, the electric field significantly enhances the contributions of the wd orbital and the Tep orbital. Therefore, the overlap between the W, d, and p orbitals of Se and Te increases. Furthermore, the degenerate state of the Te atom is disrupted, transforming it into a non-degenerate state.

[0061] This embodiment presents a technical solution for manipulating and controlling the Rashba spin splitting of the two-dimensional polar semiconductor WSeTe. By breaking the external mirror symmetry of a single layer of WSeTe, the Rashba spin splitting induced at the Γ point is analyzed. The spin splitting intensity is controlled using a biaxial strain field and a vertical electric field. The biaxial strain, by adjusting the dp orbital hybridization intensity and orbital overlap, sensitively controls the Rashba splitting amplitude and band structure properties. The vertical electric field adjustment efficiency is one-third that of the strain effect without altering the band structure. The combined manipulation of strain and electric field indicates that strain plays a dominant role; superimposing an electric field at -3% compressive strain can increase the splitting amplitude by approximately 6.5%. The strain-electric field manipulation mechanism disclosed in this invention provides a theoretical basis for spin control in two-dimensional polar semiconductors. By optimizing material symmetry and band structure design, it is expected to be applied to high-efficiency spintronic devices.

[0062] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A method for controlling Rashba spin splitting in a WSeTe monolayer, characterized in that, include: A single-layer WSeTe was selected, and its structure was optimized. The direction of the net intrinsic electric field was determined by calculating the charge density difference and work function. Based on band structure calculations with / without spin-orbit coupling, spin splitting at the Γ point is observed; The Rashba splitting characteristics were verified based on the spin texture map, and the main contributions of the Rashba splitting were analyzed based on the band projection map. Applying in-plane biaxial strain modulates the Rashba splitting intensity; Applying a vertical electric field modulates the Rashba splitting intensity; Simultaneously apply strain and electric field to modulate the Rashba splitting intensity.

2. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 1, characterized in that, The single-layer WSeTe has a two-dimensional periodic structure.

3. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 2, characterized in that, The process of determining the direction of the net intrinsic electric field through charge density difference and work function calculation includes: The work function difference is determined based on the local potential energy of the Se atomic layer and the local potential energy of the Te atomic layer.

4. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 3, characterized in that, The band structure calculation based on spin-orbit coupling (with or without spin) and the observation of spin splitting at the Γ point include: The spin splitting phenomenon was observed by calculating the band structure with and without SOC.

5. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 4, characterized in that, The verification of Rashba splitting characteristics based on spin texture maps and the analysis of the main contributions of Rashba splitting based on band projection maps include: In momentum space, the in-plane and out-of-plane spin components of the upper and lower bands are calculated to confirm the existence of Rashba spin splitting; the main contribution sources of Rashba spin splitting are analyzed based on the band projection diagram.

6. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 5, characterized in that, The method of applying in-plane biaxial strain to modulate the Rashba splitting intensity includes: Rashba spin splitting increases with increasing compressive strength and decreases with increasing tensile strength; applying in-plane biaxial strain modulates the Rashba splitting intensity.

7. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 6, characterized in that, The application of a vertical electric field to modulate the Rashba splitting intensity includes: When an electric field is applied, α R It increases slightly with the increase of electric field strength, and its increase is one-third of that of strain operation.

8. The method for regulating Rashba spin splitting in a WSeTe monolayer according to claim 7, characterized in that, The simultaneous application of strain and electric field to modulate the Rashba splitting intensity includes: Biaxial strain directly regulates orbital overlap and hybrid orbital strength through changes in lattice constant; strain dominates under the joint regulation of Rashba spin splitting by the strain electric field.

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