Performance analysis method and device for magnetically doped topological insulator with local magnetic state, and medium

Abstract

The invention discloses a magnetic doped topological insulator performance analysis method, equipment and a medium. The method comprises the following steps: introducing at least one magnetic doped element or compound into a topological insulator material; the spin symmetry of the topological insulator material is broken through the magnetic doping element or compound, so that a spin-momentum locking phenomenon is formed on the surface of the topological insulator material; and adjusting the quality parameters of the topological insulator material, and analyzing the local magnetic state change of the topological insulator material under the condition of different quality parameters in combination with a Green function. According to the invention, the electric transport characteristic is enhanced, the control on the local magnetic state is further refined, the control on the magnetic characteristic in the material is facilitated, and a theoretical basis is provided for the design and application of a novel magnetic material.

Description

Technical Field

[0001] The present invention relates to the technical field of performance analysis, and in particular to a method, device and medium for analyzing the performance of a magnetically doped topological insulator with a localized magnetic state. Background Art

[0002] Currently, low-temperature superconducting materials (such as Nb-Ti, Nb3Sn, MgB2, LaFeAsO, etc.) have been widely used in detectors, plasma magnetic confinement, superconducting energy storage, and medical magnetic resonance imaging. However, these superconducting materials need to be used at extremely low temperatures, which leads to high operating costs and limits their widespread promotion in practical applications. Based on this, there is an increasing demand for materials that can be used in a wide temperature range and have low power consumption.

[0003] As an emerging quantum material, topological insulator materials have the unique characteristics of bulk insulation and edge conductivity. Their edge states have stable conductive properties under topological protection, are not disturbed by disordered impurities on the surface of the material, and can form non-dissipative conductive channels at the edge. Therefore, topological insulators are considered to be one of the important materials for the development of future low-power electronic devices.

[0004] The conductive channels of topological insulators are protected by time reversal symmetry and usually propagate only in two directions, thus having fewer scattering channels and higher stability, which makes them have broad application prospects in low-power integrated circuits, quantum computing, and spin electronics. However, it is difficult for traditional topological insulator materials to produce quantum anomalous Hall effect in practical applications. By introducing magnetic doping elements or compounds, topological insulators can break their spin symmetry. How to adjust the localized magnetic state in topological insulators to break their time reversal symmetry and enhance their electrical transport properties has become an important research direction in this field. Summary of the invention

[0005] The purpose of the present invention is to provide a method, device and medium for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state, thereby enhancing its electrical transport properties, further refining the control of the localized magnetic state, and helping to control the magnetic properties inside the material, thus providing a theoretical basis for the design and application of new magnetic materials.

[0006] The present invention provides a magnetically doped topological insulator performance analysis method, comprising the following steps:

[0007] Introducing at least one magnetic doping element or compound into the topological insulator material; breaking the spin symmetry of the topological insulator material by the magnetic doping element or compound, so that the topological insulator material surface forms a spin-momentum locking phenomenon;

[0008] The quality parameters of the topological insulator material are adjusted, and the local magnetic state changes of the topological insulator material under different quality parameters are analyzed in combination with the Green's function.

[0009] In the above technical solution, the change of the local magnetic state of the topological insulator material under different quality parameters is analyzed in combination with the Green's function, including:

[0010] Constructing a first impurity Green's function and a second impurity Green's function; determining a self-consistent equation group of state density of impurities according to the first impurity Green's function and the second impurity Green's function;

[0011] Solving the state density self-consistent equation group, the local magnetic state change of the topological insulator material is obtained.

[0012] In the above technical solution, the change of the local magnetic state of the topological insulator material under different quality parameters is analyzed, including:

[0013] When the mass parameter is greater than 0, the mass parameter and the expansion parameter have opposite signs, and are in a trivial insulator state;

[0014] When the mass parameter is less than 0, the mass parameter and the expansion parameter have the same sign, and the magnetized area increases slowly with the increase of the mass parameter, which is in the quantum anomalous Hall insulator state.

[0015] In the above technical solution, constructing the first impurity Green's function includes:

[0016] Introducing Green's function:

[0017]

[0018] Among them, the delayed Green's function The general form of , t is time, represents the sum of the spin indices σ and σ' of the electron f, θ(t) refers to the step function, and the delay time is t' units;

[0019] Establish the equation of motion for the Green's function:

[0020]

[0021] Among them, δ(t-t') is the impulse function, which is obtained by taking the derivative of the step function.<i,j> represents the sum of the nearest neighbor atoms, and H is the Hamiltonian;

[0022] Performing Fourier transform on the above formula can obtain its form in energy ω space:

[0023]

[0024] Among them, V fis the jump strength between impurities and atoms, N is the total number of lattice points; ε σ =ε 0 +Un -σ is the local electron energy at a given U, n -σ refers to the occupation number of the added impurity with spin -σ, ε 0 is the excitation energy of the lowest quasiparticle; k is the wave vector.

[0025] In the above technical solution, constructing the second impurity Green's function includes:

[0026] Introduce a kσ , Green's function:

[0027]

[0028] Among them, a kσ , for atoms;

[0029] Perform Fourier transform to get a kσ , The expression in ω space is:

[0030]

[0031] Among them, Δ is a custom parameter, t mn is the hopping energy of adjacent atoms, is its complex conjugate.

[0032] In the above technical solution, the self-consistent equation group of the density of states of the impurities is determined according to the first impurity Green's function and the second impurity Green's function, including:

[0033] Combine the first impurity Green's function and the second impurity Green's function to determine the third impurity Green's function (η→0):

[0034]

[0035] in,

[0036] The energy spectrum E of the topological insulator system is processed to obtain the k 2 The integral and △ of :

[0037]

[0038] The third impurity Green's function can be obtained by derivation:

[0039]

[0040] The density of states of the impurity is determined as:

[0041]

[0042] in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of the d-orbital electrons of the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area or volume factor of the system;

[0043]

[0044] in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of d-orbital electrons in the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area.

[0045] In the above technical solution, the self-consistent equations of the state density of the impurities are solved by the fsolve algorithm, and the optimal number of grid points is taken to obtain the solution of specific parameters.

[0046] The above technical solution also includes:

[0047] By adjusting the quality parameters, topological insulator materials can achieve conversion between quantum anomalous Hall effect and ordinary insulating state in different magnetization regions.

[0048] The present invention provides a device, comprising multiple processors, a memory, and a computer program stored in the memory and executable on the processor. When the multiple processors execute the computer program, a method for analyzing the performance of a magnetically doped topological insulator having a localized magnetic state as described in any one of the above items is implemented.

[0049] The present invention provides a storage medium having a computer program stored thereon, wherein when the computer program is executed, a method for analyzing the performance of a magnetically doped topological insulator having a localized magnetic state as described in the above item is implemented.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention provides a magnetic doped topological insulator performance analysis method, device, and medium with a localized magnetic state, introduces magnetic doping elements, and adjusts quality parameters, so as to achieve precise control of the localized magnetic state in the topological insulator, and further refine the control of the localized magnetic state. Different magnetic phase transitions are exhibited under different quality parameter conditions, which helps to understand and control the magnetic properties inside the material, and provides a theoretical basis for the design and application of new magnetic materials, thereby bringing lower power consumption and more stable electronic transmission characteristics, and has broad application prospects in the fields of quantum computing and sensing. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of a flow chart of an embodiment of the present invention.

[0053] Figure 2 Magnetic and non-magnetic boundary diagrams for different mass parameters m according to an embodiment of the present invention.

[0054] Figure 3 Schematic diagram of the relationship between the impurity occupation number (n↓(μ), n↑(μ)) and the magnetic susceptibility χ of the topological insulator system according to an embodiment of the present invention and the Fermi energy μ. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] Embodiment 1:

[0057] This embodiment provides a method for analyzing the performance of a magnetically doped topological insulator with a localized magnetic state, further refining the control of the localized magnetic state, helping to control the magnetic properties inside the material, and providing a theoretical basis for the design and application of new magnetic materials.

[0058] Specifically, the method includes:

[0059] Step S1, introducing at least one magnetic doping element or compound into a topological insulator material; breaking the spin symmetry of the topological insulator material by the magnetic doping element or compound, so that a spin-momentum locking phenomenon is formed on the surface of the topological insulator material.

[0060] Topological insulators can be viewed as a superposition of two time-reversal symmetric Hubbard models. Therefore, when a long-range ferromagnetic order is introduced into a two-dimensional topological insulator, two spirals can be observed. By destroying one of the edge states, the quantum anomalous Hall effect is achieved. When materials used in the electronic field work normally, energy is lost in the form of heat dissipation, while topological insulator materials are insulators inside and have conductive properties outside; electrons are transmitted through the surface in a spin manner, and the heat dissipation phenomenon of the material will not occur, greatly improving the energy transmission efficiency.

[0061] Magnetically doped topological insulators break the spin symmetry of their own materials by introducing magnetic elements or compounds, making their surface state electrons closely related to the direction of motion, forming a spin-momentum locking phenomenon. This characteristic makes topological insulators exhibit unique electrical transport properties under the action of a magnetic field.

[0062] The band structure of topological insulator materials has good topological characteristics. Impurities and defects inside the material have little effect on it, and the structure is anisotropic. As shown in the following two-dimensional massive Dirac model:

[0063] H d =v(k y σ x +ηk x σ y )+(m / 2-αk 2 )σ z

[0064] H d represents the Hamiltonian of a two-dimensional topological system, v represents the velocity, parameter η=1, k x , k y is the component of the wave vector k in the xy direction, σ x , σ y , σ z is the component of the Pauli matrix in the xyz direction, m is the quality parameter in the added independent term, that is, the gap, and α is the expansion parameter.

[0065] When m and α in the model change from the same sign to different signs, the topological material system undergoes band inversion and undergoes a topological phase transition from the quantum anomalous Hall insulator state to the two-dimensional ordinary insulator state.

[0066] After the topological insulator system adsorbs impurities, the Hamiltonian consists of three parts:

[0067] H=H d +H i +H f

[0068] Considering the interaction between adsorbed impurities and the nearest atoms, the Hamiltonian is:

[0069]

[0070] Among them, H i represents the interaction between the adsorbed impurity electrons and the nearest atoms, where and f σ is the impurity electron creation and annihilation operator, the spin index of the operator is σ(=↑↓), V f is the jump strength between the impurity and the atom. and a σ (Rl) is the creation and annihilation operator of A atom, and Rl is the position of the atom.

[0071] H in the system Hamiltonian f Represents the coupling Hamiltonian between impurity electrons:

[0072]

[0073] H f represents the coupling Hamiltonian between impurity electrons, ε σ =ε 0 +Un -σ is the local electron energy at a given U, n -σ Refers to the occupation number of the added impurity with spin -σ, ∈ σ is the excitation energy, ∈0 is the lowest excitation energy of the quasiparticle.

[0074] Step S2, adjusting the quality parameter of the topological insulator material, and analyzing the change of the local magnetic state of the topological insulator material under different quality parameters in combination with the Green's function.

[0075] By changing the sign of the quality parameter m in the independent term, the magnetic phase transition caused by the hybridization between impurity electrons and system transport electrons is analyzed. The specific analysis is as follows:

[0076] The change of the local magnetic state of the topological insulator material under different quality parameters is analyzed in combination with the Green's function, including:

[0077] Constructing a first impurity Green's function and a second impurity Green's function; determining a self-consistent equation group of state density of impurities according to the first impurity Green's function and the second impurity Green's function;

[0078] Solving the state density self-consistent equation group, the local magnetic state change of the topological insulator material is obtained.

[0079] Wherein, constructing the first impurity Green's function includes:

[0080] Introducing Green's function:

[0081]

[0082] Among them, the delayed Green's function The general form of , t is time, represents the sum of the spin indices σ and σ' of the electron f, θ(t) refers to the step function, and the delay time is t' units;

[0083] Establish the equation of motion for the Green's function:

[0084]

[0085] Among them, δ(t-t') is the impulse function, which is obtained by taking the derivative of the step function.<i,j> represents the sum of the nearest neighbor atoms, and H is the Hamiltonian;

[0086] Performing Fourier transform on the above formula can obtain its form in energy ω space:

[0087]

[0088] Among them, V f is the jump strength between impurities and atoms, N is the total number of lattice points; ε σ =ε 0 +Un -σ is the local electron energy at a given U, n -σ refers to the occupation number of the added impurity with spin -σ, ε 0 is the excitation energy of the lowest quasiparticle; k is the wave vector.

[0089] Construct the second impurity Green's function, including:

[0090] Introduce a kσ , Green's function:

[0091]

[0092] Among them, a kσ , for atoms;

[0093] Perform Fourier transform to get a kσ , The expression in ω space is:

[0094]

[0095] Among them, Δ is a custom parameter, t mn is the hopping energy of adjacent atoms, is its complex conjugate.

[0096] Determining a self-consistent equation group of impurity state density according to the first impurity Green's function and the second impurity Green's function includes:

[0097] Combine the first impurity Green's function and the second impurity Green's function to determine the third impurity Green's function (η→0):

[0098]

[0099] in,

[0100] The energy spectrum E of the topological insulator system is processed to obtain the k 2 The integral and △ of :

[0101]

[0102] The third impurity Green's function can be obtained by derivation:

[0103]

[0104] The density of states of the impurity is determined as:

[0105]

[0106] in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of the d-orbital electrons of the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area;

[0107]

[0108] in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of d-orbital electrons in the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area.

[0109] The fsolve algorithm is used to solve the self-consistent equations, and the optimal number of grid points is selected to obtain the solution for a specific parameter, and n is obtained. σ are two solutions to the self-consistent equations for the density of states. ↑ and n ↓ The difference between them from zero to non-zero represents the observed change from the non-magnetic phase to the magnetic phase.

[0110] Specifically, Figure 2Figure 2 shows the magnetic and non-magnetic boundary diagrams for different mass parameters m, m<0 (a) and m>0 (b), where the parameters are set: ε0=0.3eV, Vf=1.0eV and α=0.1eV, black: |m|=0.1eV, red: |m|=0.3eV, blue: |m|=0.8eV. The boundary of the magnetic and non-magnetic impurity states at α=0.1eV at mass parameters m<0 and m>0 varies with parameters x and y, ε 0 =0.3eV. When the mass parameter |m| in the system independent term gradually increases, the impurity magnetization area slowly decreases during the evolution process. In the m<0 independent term, the mass parameter and the expansion parameter keep opposite signs, and the system is in a trivial insulator state. Due to the properties of the Dirac quantum, the local state density near the edge of the energy band gap is induced, and the influence of the impurity enhances the coupling effect in the gap, enhances the renormalization density of the impurity energy level, and reduces the interval between them, and the impurity magnetization area decreases accordingly.

[0111] For m>0, the parameter m in the mass term has the same sign as α, and the impurity magnetization area increases slowly with the increase of the mass parameter m; the system is in a quantum anomalous Hall insulator state, and the inversion between the conduction band and the valence band destroys the renormalization of the impurity energy dominated by Dirac quasiparticles. When magnetic impurities enter the energy gap, the inversion between the conduction band and the valence band causes it to be slightly renormalized, and the impurities are also easily magnetized. The impact on the impurities in the energy gap is decreasing, and the impurity magnetization area will gradually increase with the increase of m. The electronic behavior on the special edge state of the topological insulator becomes intense. From the figure, it can be seen that the deviation of the boundary line of the magnetic transition to the y-axis is slowly increasing, which reflects the characteristics of the Dirac particles of the system after the addition of magnetic impurities.

[0112] The parameter space x = DΓ / U, y = (μ-ε 0 ) / U describes the boundary between magnetic and non-magnetic impurity states. The parameter Γ in the parameter space describing the magnetic boundary refers to the expansion constant of the density of states. Figure 3 The relationship between the impurity occupation number (n↓(μ), n↑(μ)) and the magnetic susceptibility χ of the topological insulator system and the Fermi energy μ, parameter settings: ∈0=0.3eV and α=0.1eV, Figures (a) and (c) for m<0, black: m=-0.1eV, red: m=-0.3eV, blue: m=-1.5eV. Figures (b) and (d) for m>0, black: m=0.1eV, red: m=0.3eV, blue: m=0.8eV. The solution of n↓(μ)=n↑(μ) shows the impurity occupation number n corresponding to the Fermi energy μ in the magnetization bubble σ, a bubble diagram showing the impurity magnetization intensity. The other is the magnetic susceptibility χ relative to the Fermi energy μ. There are two asymmetric peaks in the relationship between the magnetic induction intensity and the Fermi energy. These peaks represent the intensity of the system's magnetic transition.

[0113] from Figure 3 In the figure, we can see two asymmetric peaks of the system energy, located at the left and right edges of the magnetized bubble. The transition position from the magnetic solution to the non-magnetic solution is changing, but the Fermi energy at the location where the change occurs is always greater than μ = 0.3 eV. As the mass parameter m continues to increase, the location where the change occurs begins to be slightly less than μ = 0.3 eV. Figure 3 (a) The system is in a normal insulating state. Figure 3 (b) The system is in a quantum anomalous Hall insulator state. In the high energy state, the impurity magnetization is more sensitive to the magnetic field and is more easily changed by external operations. As the quality parameter m increases, the peak on the left will increase, while that on the right will decrease. The change is relatively obvious. This transition can be understood from the renormalization of the topological non-trivial characteristic edge states of topological insulators. The special edge states make electrons more easily magnetized. This also shows that the quality parameter m can be used to manipulate the sensitivity of impurity magnetization to external magnetic fields.

[0114] Figure 3 (a) Magnetization line parameters correspond to Figure 3 (a) In Figure 3 (b) shows the relationship between the number of impurity spin level occupancy and μ for α>0 and m>0. A huge rectangular bubble can be seen, indicating that a 0.9μ B The magnetized bubble moves toward lower energy as |m| increases, but its size remains essentially unchanged.

[0115] This application couples magnetic impurities with electrons in a topological insulator system. After adding magnetic impurities, two different phenomena will occur when the system parameters are changed. The system will undergo a transition from a quantum anomalous Hall state to an ordinary insulating state. In this process, a transition change and magnetic change different from that caused by doping magnetic impurities in graphene will occur.

[0116] Changing the value of the mass parameter m to positive or negative will not cause the difference in magnetization areas to disappear, which is also an important sign of parity anomaly. From the magnetic moment diagram, the mass parameter can be used to manipulate the sensitivity of impurity magnetization to the external magnetic field, which is related to the drastic change in the renormalization of the impurity energy at the edge of the system. In the field of quantum computing, the realization of quantum computers can rely on the superposition of quantum states to improve computing efficiency and computing power. At the same time, the characteristics of topological insulators themselves can realize low-power devices without heat dissipation losses; quantum anomalous Hall insulators can be used in the military and medical fields to detect weak electromagnetic signals under certain conditions. Moreover, these differences can be used to detect the characteristics of parity anomalies in topological quantum materials, providing reference value for studying topological insulator materials in the application of spin electronics.

[0117] The present invention can accurately analyze the formation of local magnetic states of materials by introducing physical models and formulas such as Hamiltonian, Green's function and density of states (DOS). Through the calculation and verification of these formulas, the influence of magnetic doping on topological insulator materials can be more intuitively observed, providing a reliable basis for optimizing material performance. By adjusting the sign and doping concentration of the quality parameter m, the phase change regulation of topological insulators from quantum anomalous Hall states to ordinary insulating states is realized. Compared with traditional methods, this method can more flexibly control the quantum states of materials through the solution of self-consistent equations and the regulation of Hamiltonian formulas, laying the foundation for realizing low-power electronic devices. At the same time, the electrical properties, quantum phase transitions, spin polarization and local magnetic states of magnetic doped topological insulator materials can be analyzed more comprehensively and accurately, with the advantages of high efficiency, flexibility and accuracy, providing scientific support and theoretical basis for the application of such materials in the fields of low-power electronics, spin electronics and quantum computing.

[0118] The unique edge state conductivity of topological insulators can effectively reduce heat dissipation and improve energy transmission efficiency. For example, in outdoor energy storage systems and intelligent battery management systems, especially in the applications of photovoltaic energy storage and mobile power supplies, the low power consumption characteristics of topological insulators can be used to design more energy-saving battery management solutions. More efficient energy management and storage can be achieved through low heat dissipation. At the same time, the magnetic doping characteristics and spin-momentum locking effect in topological insulators can provide technical support for spin electronics for outdoor energy storage products, thereby reducing energy loss in battery management. The characteristics of spin-momentum locking have the potential to extend battery life, optimize the charging process, and improve the stability of energy storage equipment, so that the product can still maintain high efficiency under high load conditions. The stability and low power consumption characteristics of topological insulators can be combined with energy storage products, intelligent monitoring and adaptive power dispatching functions to provide more efficient and intelligent power management solutions.

[0119] Based on the same inventive concept, the present invention further provides a storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the aforementioned method are implemented.

[0120] Among them, the computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form, etc. Computer readable media may include: any entity or device capable of carrying computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in computer readable media can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer readable media do not include electric carrier signals and telecommunication signals.

[0121] The present invention can be used in many general or special computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.

[0122] The present application also provides an electronic device, comprising a memory, multiple processors, and a program stored in the memory, wherein the program is configured to be executed by the processors, and the steps of the above method are implemented when the multiple processors execute the program.

[0123] In addition, the present invention also provides a storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the aforementioned method are implemented. The present invention can be used in many general or special computing system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, multi-processor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc.

[0124] The device in this embodiment and the method in the aforementioned embodiment are two aspects based on the same inventive concept. The method implementation process has been described in detail above, so those skilled in the art can clearly understand the structure and implementation process of the system in this embodiment based on the aforementioned description. For the sake of brevity of the specification, they will not be repeated here.

[0125] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A magnetically doped topological insulator performance analysis method, characterized in that: The following steps are involved: Introducing at least one magnetic doping element or compound into the topological insulator material; breaking the spin symmetry of the topological insulator material by the magnetic doping element or compound, so that the topological insulator material surface forms a spin-momentum locking phenomenon; The quality parameters of the topological insulator material are adjusted, and the local magnetic state changes of the topological insulator material under different quality parameters are analyzed in combination with the Green's function.

2. A magnetic-doped topological insulator performance analysis method with a localized magnetic state according to claim 1, characterized in that: The change of the local magnetic state of the topological insulator material under different quality parameters is analyzed in combination with the Green's function, including: Constructing a first impurity Green's function and a second impurity Green's function; determining a self-consistent equation group of state density of impurities according to the first impurity Green's function and the second impurity Green's function; Solving the state density self-consistent equation group, the local magnetic state change of the topological insulator material is obtained.

3. A magnetic-doped topological insulator performance analysis method with a localized magnetic state according to claim 1, characterized in that: Analysis of the changes in the local magnetic state of the topological insulator material under different quality parameters includes: When the mass parameter is greater than 0, the mass parameter and the expansion parameter have opposite signs, and are in a trivial insulator state; When the mass parameter is less than 0, the mass parameter and the expansion parameter have the same sign, and the magnetized area increases slowly with the increase of the mass parameter, which is in the quantum anomalous Hall insulator state.

4. A magnetic-doped topological insulator performance analysis method with a localized magnetic state according to claim 2, characterized in that: Construct the first impurity Green's function, including: Introducing Green's function: Among them, the delayed Green's function The general form of , t is time, represents the sum of the spin indices σ and σ' of the electron f, θ(t) refers to the step function, and the delay time is t' units; Establish the equation of motion for the Green's function: Among them, δ(t-t') is the impulse function, which is obtained by taking the derivative of the step function.<i,j> represents the sum of the nearest neighbor atoms, and H is the Hamiltonian; Performing Fourier transform on the above formula can obtain its form in energy ω space: Among them, V f is the jump strength between impurities and atoms, N is the total number of lattice points; ε σ =ε0+Un -σ is the local electron energy at a given U, n -σ It refers to the occupation number of the added impurity with spin -σ, ε0 is the excitation energy of the lowest quasiparticle; k is the wave vector.

5. A magnetic-doped topological insulator performance analysis method with a localized magnetic state according to claim 4, characterized in that: Construct the second impurity Green's function, including: Introduce a kσ , Green's function: Among them, a kσ , for atoms; Perform Fourier transform to get a kσ , The expression in ω space is: Among them, Δ is a custom parameter, t mn is the hopping energy of adjacent atoms, is its complex conjugate.

6. A method for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state according to claim 5, characterized in that: Determining a self-consistent equation group of impurity state density according to the first impurity Green's function and the second impurity Green's function includes: Combine the first impurity Green's function and the second impurity Green's function to determine the third impurity Green's function (η→0): in, The energy spectrum E of the topological insulator system is processed to obtain the integral and △ of k2: The third impurity Green's function can be obtained by derivation: The density of states of the impurity is determined as: in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of the d-orbital electrons of the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area or volume factor of the system; in: represents the number of states occupied at unit energy levels with different spins, D is the cutoff energy, U represents the mutual correlation energy of d-orbital electrons in the atom; f(ω) is the Fermi distribution function; α is the expansion parameter; v is the velocity, m is the mass parameter, C is the expansion constant of the state density, and S is the area.

7. A method for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state according to claim 6, characterized in that: The fsolve algorithm is used to solve the self-consistent equations of the state density of the impurity, and the optimal number of grid points is taken to obtain the solution of specific parameters.

8. A method for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state according to claim 2, characterized in that: Also includes: By adjusting the quality parameters, topological insulator materials can achieve conversion between quantum anomalous Hall effect and ordinary insulating state in different magnetization regions.

9. A device, characterized in that: The invention comprises a plurality of processors, a memory and a computer program stored in the memory and executable on the processor. When the plurality of processors execute the computer program, a method for analyzing the performance of a magnetically doped topological insulator having a localized magnetic state as described in any one of claims 1 to 8 is implemented.

10. A storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed, a method for analyzing the performance of a magnetically doped topological insulator with a localized magnetic state as described in any one of claims 1 to 8 is implemented.

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