Method, device and medium for analyzing performance of magnetic-doped topological insulator with localized magnetic state

Abstract

The application discloses a kind of magnetic doping topological insulator performance analysis method, equipment, medium, comprising: introducing at least one magnetic doping element or compound in topological insulator material;Break the spin symmetry of topological insulator material by the magnetic doping element or compound, so that topological insulator material surface forms the phenomenon of spin-momentum locking;Adjust the quality parameter of the topological insulator material, combine Green function analysis under different quality parameters, the local magnetic state change of the topological insulator material.The application enhances its electrical transport characteristics, further refines the control of local magnetic state, helps to control the magnetic properties inside material, provides theoretical basis for the design and application of new magnetic material.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of performance analysis, in particular to a performance analysis method, device and medium of a magnetic-doped topological insulator with a local magnetic state. BACKGROUND

[0002] At present, low-temperature superconducting materials such as Nb-Ti, Nb3Sn, MgB2 and LaFeAsO have been widely used in fields such as 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 application in practical applications. Therefore, there is an increasing demand for materials that can be used in a wide temperature range and have low power consumption.

[0003] As a new quantum material, the topological insulator material has the unique characteristics of bulk state insulation and edge conduction. The edge state is stable under topological protection and is not disturbed by disordered impurities on the surface of the material, and can form a non-dissipative conduction channel on the edge. Therefore, the topological insulator is considered to be one of the important materials for the development of low-power electronic devices in the future.

[0004] The conduction channel of the topological insulator is protected by time reversal symmetry and usually propagates in only two directions, thereby having fewer scattering channels and higher stability, which makes it have broad application prospects in the fields of low-power integrated circuits, quantum computing and spin electronics. However, traditional topological insulator materials are difficult to produce quantum anomalous Hall effect in practical applications. By introducing magnetic doping elements or compounds, the topological insulator can break its spin symmetry. How to adjust the local magnetic state in the topological insulator to break its time reversal symmetry and enhance its electrical transport characteristics has become an important research direction in the field. SUMMARY

[0005] The purpose of the present application is to provide a performance analysis method, device and medium of a magnetic-doped topological insulator with a local magnetic state, which enhances the electrical transport characteristics and further refines the control of the local magnetic state, helps to control the magnetic properties inside the material, and provides a theoretical basis for the design and application of new magnetic materials.

[0006] The present application provides a performance analysis method of a magnetic-doped topological insulator, 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 through the magnetic doping element or compound, so that the spin-momentum locking phenomenon is formed on the surface of the topological insulator material;

[0008] Adjusting a mass parameter of the topological insulator material, and analyzing a local magnetic state change of the topological insulator material under different mass parameters by combining a Green function.

[0009] In the technical solution, the local magnetic state change of the topological insulator material under different mass parameters is analyzed by combining a Green function, and the analysis includes:

[0010] A first impurity Green function and a second impurity Green function are constructed, and a state density self-consistent equation set of impurities is determined according to the first impurity Green function and the second impurity Green function.

[0011] The state density self-consistent equation set is solved to obtain the local magnetic state change of the topological insulator material.

[0012] In the technical solution, the analysis of the local magnetic state change of the topological insulator material under different mass parameters includes:

[0013] When the mass parameter is greater than 0, the mass parameter and the expansion parameter keep opposite signs, and the topological insulator material is in a trivial insulator state.

[0014] When the mass parameter is less than 0, the mass parameter and the expansion parameter keep the same sign, the magnetization region slowly increases with the increase of the mass parameter, and the topological insulator material is in a quantum anomalous Hall insulator state.

[0015] In the technical solution, the first impurity Green function is constructed, and the construction includes:

[0016] The Green function is introduced as:

[0017]

[0018] The general form of the time-delayed Green function is G (t, t') = -i , t is time, , θ (t) is a step function, and t' is a time delay unit.

[0019] The motion equation of the Green function is established as:

[0020]

[0021] In the equation, δ (t-t') is an impulse function, which is derived from the derivative of the step function, <i,j> represents the summation of the nearest neighbor atoms, and H is the Hamiltonian.

[0022] The Fourier transform of the above equation can obtain the form in the energy ω space:

[0023]

[0024] In the equation, V fis the hopping strength between impurities and atoms, N is the total number of lattice points; epsilon σ = epsilon0 + Un -σ is the local electron energy in the case of given U, n -σ is the occupation number of the spin of the added impurity, epsilon0 is the lowest quasi-particle excitation energy; k is the wave vector.

[0025] In the technical scheme, the second impurity Green function is constructed, comprising:

[0026] The Green function of a kσ , is introduced:

[0027]

[0028] Wherein, a kσ , is an atom;

[0029] The Fourier transform is carried out to obtain the expression of a kσ , in the omega space:

[0030]

[0031] Wherein, Delta is a self-defined parameter, t mn is the hopping energy of adjacent atoms, is the conjugate complex thereof.

[0032] In the technical scheme, the state density self-consistent equation of the impurity is determined according to the first impurity Green function and the second impurity Green function, comprising:

[0033] The first impurity Green function and the second impurity Green function are solved to determine the third impurity Green function (eta to 0):

[0034]

[0035] Wherein,

[0036] The spectrum E of the topological insulator system is processed to obtain the integral of k2 and Delta:

[0037]

[0038] After derivation, the third impurity Green function can be obtained:

[0039]

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

[0041]

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

[0043]

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

[0045] In the technical solution, the state density self-consistent equation of the impurity is solved by the fsolve algorithm, and the optimal number of grid points is taken to obtain a solution of a specific parameter.

[0046] In the technical solution, the method further comprises:

[0047] By adjusting the mass parameter, the conversion between the quantum anomalous Hall effect and the ordinary insulating state of the topological insulator material is realized in different magnetization regions.

[0048] The application provides a device comprising a plurality of processors, a memory, and a computer program stored on the memory and executable on the processors, wherein the plurality of processors implement the method for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state according to any one of the preceding embodiments when executing the computer program.

[0049] The application provides a storage medium having a computer program stored thereon, wherein the computer program implements the method for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state according to the preceding embodiment when executed.

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

[0051] The application provides a method, device, and medium for analyzing the performance of a magnetic-doped topological insulator with a localized magnetic state, introduces a magnetic-doped element, and adjusts the mass parameter, so that the localized magnetic state in the topological insulator can be accurately controlled, and the control of the localized magnetic state is further refined. Different magnetic phase transitions are exhibited under different mass parameter conditions, which helps to understand and control the magnetic properties inside the material, provides a theoretical basis for the design and application of new magnetic materials, and thus brings lower power consumption, more stable electronic transmission characteristics, and a wide application prospect in the field of quantum computing and sensing. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 A flowchart of an embodiment of the present application.

[0053] Figure 2 A magnetic and non-magnetic boundary map for different quality parameters m of an embodiment of the present application.

[0054] Figure 3 A schematic diagram of the relationship between the impurity occupation number (n↓(μ), n↑(μ)) and the magnetic susceptibility χ of a topological insulator system of an embodiment of the present application as a function of the Fermi energy μ. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the scope of the present application.

[0056] Embodiment one:

[0057] The embodiment provides a performance analysis method for a magnetic doped topological insulator with a local magnetic state, which further refines the control of the local magnetic state and helps to control the magnetic properties inside the material, thereby providing a theoretical basis for the design and application of new magnetic materials.

[0058] Specifically, the method comprises the following steps.

[0059] In step S1, at least one magnetic doped element or compound is introduced into a topological insulator material; the spin symmetry of the topological insulator material is broken by the magnetic doped element or compound, so that a spin-momentum locking phenomenon is formed on the surface of the topological insulator material.

[0060] The topological insulator can be regarded as the superposition of two time-reversal symmetry Huber models. Therefore, when a long-range ferromagnetic order is introduced into a two-dimensional topological insulator, two spiral lines can be observed. By destroying one of the edge states, a quantum anomalous Hall effect is achieved. The material applied in the electronic field loses energy in the form of heat dissipation when it is normally working. The topological insulator material is an insulator inside and has conductive properties outside; the electrons are transmitted in the form of spin on the surface, and the heat dissipation phenomenon of the material will not occur, so that the energy transmission efficiency is greatly improved.

[0061] The magnetic doped topological insulator breaks the spin symmetry of its own material by introducing a magnetic element or compound, so that the surface state electrons are closely related to the direction of motion, forming a spin-momentum locking phenomenon. This characteristic makes the topological insulator exhibit unique electrical transport properties under the action of a magnetic field.

[0062] The band structure of topological insulator material has good topological characteristics, and the impurities and defects inside the material have little effect on it. This structure presents anisotropy. 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 is the Hamiltonian of a two-dimensional topological system, v represents the velocity, the parameter η = 1, k x , k y are the components of the wave vector k in the xy direction, σ x , σ y , σ z are the components of the Pauli matrix in the xyz direction, m is the mass parameter in the 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 experiences a topological phase transition from a quantum anomalous Hall insulator state to a two-dimensional ordinary insulator state.

[0066] The Hamiltonian of the topological insulator system after adsorbing impurities is composed of three parts:

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

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

[0069]

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

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

[0072]

[0073] H f represents the coupling Hamiltonian between impurity electrons, ε σ = ε0+ Un -σ is the local electron energy in the presence of U, n -σ denotes the number of impurity spin -σ occupation, ∈ σ is the excitation energy, ∈0 is the excitation energy of the lowest quasi-particle.

[0074] Step S2, adjusting the mass parameter of the topological insulator material, combining the Green function analysis to analyze the change of the local magnetic state of the topological insulator material under different mass parameters.

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

[0076] Combining the Green function analysis under different mass parameters, the change of the local magnetic state of the topological insulator material is analyzed, including:

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

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

[0079] Among them, the first impurity Green function is constructed, including:

[0080] Introducing the Green function:

[0081]

[0082] Where the general form of the time-delayed Green function is t is time, represents the sum of f electrons whose spin index is σ, σ', θ(t) is a step function, and the time delay t' unit;

[0083] The motion equation of the Green function is established:

[0084]

[0085] Where δ(t-t') is the impulse function, which is derived from the derivative of the step function, <i,j> represents the summation of the nearest neighbor atoms, and H is the Hamiltonian;

[0086] The Fourier transform of the above formula can be obtained in the energy ω space:

[0087]

[0088] where V f is the hopping 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 is the occupation number of the spin -σ of the added impurity, ε0is the lowest quasi-particle excitation energy; k is the wave vector.

[0089] constructing a second impurity Green function, comprising:

[0090] introducing the Green function of a kσ , :

[0091]

[0092] where a kσ , is an atom;

[0093] performing Fourier transform to obtain the expression of a kσ , in ω space:

[0094]

[0095] where Δ is a self-defined parameter, t mn is the hopping energy of adjacent atoms, is the conjugate complex thereof.

[0096] determining the state density self-consistent equation of the impurity according to the first impurity Green function and the second impurity Green function, comprising:

[0097] determining the third impurity Green function (η→0) by combining the first impurity Green function and the second impurity Green function:

[0098]

[0099] where,

[0100] processing the spectrum E of the topological insulator system to obtain the integral of k2 and Δ:

[0101]

[0102] the third impurity Green function can be obtained through derivation:

[0103]

[0104] the state density of the impurity is determined as:

[0105]

[0106] in: denoted by ω, D is the cutoff energy, U represents the correlation energy of electrons in the d orbitals of an 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 density of states; and S is the area.

[0107]

[0108] in: ω represents the number of states occupied by a unit energy level with different spins, D is the cutoff energy, U represents the correlation energy of electrons in the d orbitals of an 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 density of states, and S is the area.

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

[0110] Specifically, such as Figure 2 As shown, the magnetic and nonmagnetic boundary diagrams for different mass parameters m are m<0(a) and m>0(b), where the parameters are set as follows: ∈0=0.3eV, Vf=1.0eV and α=0.1eV, black: |m|=0.1eV, red: |m|=0.3eV, blue: |m|=0.8eV. The boundary between the magnetic and nonmagnetic impurity states at mass parameters m<0 and m>0 at α=0.1eV varies with parameters x and y, ε0=0.3eV. As the mass parameter |m| in the independent terms of the system gradually increases, the impurity magnetization region slowly decreases during the evolution. In the independent terms of m<0, the mass parameter and expansion parameter maintain opposite signs, and the system is in a trivial insulator state. Due to the properties of Dirac quanta, the local density of states near the band gap edge is induced. The influence of impurities enhances the coupling within the gap, increasing the renormalization density of the impurity energy levels and reducing the gap between them, thus decreasing the impurity magnetization region.

[0111] For m > 0, the parameter m in the mass term and the sign of a remain the same, and the magnetization region of the impurity increases slowly with the increase of the mass parameter m; the system is in the 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 quasi-particles. When the magnetic impurity enters the energy gap, the inversion between the conduction band and the valence band makes it slightly renormalized, and the impurity is also easily magnetized. The influence of the impurity in the energy gap is decreasing, and the magnetization region of the impurity gradually increases with the increase of m. The electronic behavior on the special edge state of the topological insulator becomes strong, and it can be seen from the figure that the deviation of the boundary line of the magnetic transition from the y-axis is slowly increasing, which reflects the characteristics of the Dirac particles of the system after the addition of the magnetic impurity.

[0112] The parameter space x = DΓ / U, y = (μ-ε0) / U is introduced to describe the boundary between the magnetic and non-magnetic impurity states. The parameter Γ in the parameter space describing the magnetic boundary refers to the expansion constant of the state density. Figure 3 The relationship between the impurity occupation number (n↓(μ), n↑(μ)) and the magnetic susceptibility χ of the topological insulator system with the Fermi energy μ, and the parameter settings: ∈0=0.3 eV and α=0.1 eV. In figures (a) and (c), for m<0, black: m=-0.1 eV, red: m=-0.3 eV, and blue: m=-1.5 eV. In figures (b) and (d), for m>0, black: m=0.1 eV, red: m=0.3 eV, and blue: m=0.8 eV. The solution of n↓(μ)=n↑(μ) shows the impurity occupation number n corresponding to the Fermi energy μ in the magnetization bubble σ , indicating the bubble diagram of the magnetization intensity of the impurity. The other is the magnetic susceptibility χ with respect to the Fermi energy μ, and two asymmetric peaks appear in the relationship between the magnetic induction intensity and the Fermi energy, which represent the strength of the magnetic transition of the system.

[0113] From Figure 3 , it can be seen that there are two asymmetric peaks in the system energy, located at the left edge and the right edge of the magnetization bubble, respectively. The transition position of the magnetic solution to the non-magnetic solution changes, but the Fermi energy is greater than μ=0.3 eV, and as the mass parameter m continues to increase, the position where the change occurs is slightly less than μ=0.3 eV. Figure 3 (a) The system is in the ordinary insulator state, Figure 3 (b) The system is in the quantum anomalous Hall insulator state, and in the high-energy state, the impurity magnetization is more sensitive to the magnetic field and is more easily changed by external operation. With the increase of the mass parameter m, the left peak will increase, and the right peak will decrease, and the change is relatively obvious. This transition can be understood from the renormalization of the topologically nontrivial edge state of the topological insulator, and the special edge state makes the electron more easily magnetized, which also indicates that the mass parameter m can be used to manipulate the sensitivity of the impurity magnetization to the external magnetic field.

[0114] Figure 3 (a) magnetization line parameter correspondence Figure 3 (a). In Figure 3 The relationship between the impurity spin energy level occupation number and mu is plotted in (b) for alpha>0 and m>0. A huge rectangular bubble can be seen, indicating that a 0.9 mu B Strong magnetic moment is formed in almost the entire magnetic region. The magnetized bubble moves in the direction of low energy as |m| increases, but its size remains essentially unchanged.

[0115] The present application adds magnetic impurities to the system of magnetic impurities and topological insulators, and changes the system parameters after adding magnetic impurities. Two different phenomena will occur, the system will undergo a transition from quantum anomalous Hall state to trivial insulating state, and in this process, a transition change different from the doping of magnetic impurities in graphene and magnetic change is produced.

[0116] The difference in the magnetization region will not disappear by changing the value of the mass parameter m to be positive or negative, 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 external magnetic field, which is related to the dramatic change in the regularization of impurity energy at the edge of the system. In the field of quantum computing, the implementation of quantum computers can rely on the superposition of quantum states to improve the efficiency and computing power of the operation. At the same time, the characteristics of topological insulators can realize low-power power devices without heat loss; Quantum anomalous Hall insulator can be used to detect weak electromagnetic signals in military and medical fields under certain conditions. More, these differences can be used to detect the characteristics of parity anomaly in topological quantum materials, and provide reference value for the study of topological insulator materials in spintronics applications.

[0117] The present application can accurately analyze the formation of local magnetic state of the material 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 of the mass parameter m and the doping concentration, the phase transition control of topological insulator from quantum anomalous Hall state to ordinary insulating state is realized. Compared with the traditional method, the present method can more flexibly control the quantum state of the material by solving the self-consistent equation and adjusting the Hamiltonian formula, laying a foundation for realizing low-power electronic devices. At the same time, it can more comprehensively and accurately analyze the electrical performance, quantum phase transition, spin polarization and local magnetic state of the magnetic doping topological insulator material, with the advantages of high efficiency, flexibility and accuracy, providing scientific support and theoretical basis for the application of such materials in low-power electronics, spintronics and quantum computing fields.

[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 photovoltaic energy storage and mobile power applications, the low-power consumption characteristics of topological insulators can be used as a reference to design more energy-efficient battery management solutions. Through low heat dissipation, more efficient energy management and storage can be achieved. At the same time, the magnetic doping characteristics and spin-momentum locking effect in topological insulators can provide technical support for spin electronics in 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 scheduling functions to provide more efficient and intelligent power management solutions.

[0119] Based on the same inventive concept, the application also provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the foregoing method.

[0120] The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate forms, etc. The computer readable medium can include any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer readable medium 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, the computer readable medium does not include electrical carrier signals and telecommunication signals.

[0121] The application 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 electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc.

[0122] The application also provides an electronic device, which includes a memory, a plurality of processors, and a program stored in the memory, the program being configured to be executed by the processors, and the plurality of processors implementing the steps of the above method when executing the program.

[0123] In addition, the present application further provides a storage medium, wherein the storage medium stores a computer program, and the computer program is executed by a processor to realize the steps of the foregoing method. The present application can be used in many general or special computer system environments or configurations. For example, personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.

[0124] The device in the embodiment and the method in the foregoing embodiment are two aspects based on the same inventive concept, and the implementation process of the method has been described in detail in the foregoing. Therefore, the structure and implementation process of the system in the embodiment can be clearly understood by those skilled in the art according to the foregoing description. For the sake of brevity of the description, no further description is given here.

[0125] Although the embodiments of the present application have been shown and described, it is understood that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the performance of magnetically doped topological insulators with localized magnetic states, characterized in that, Includes the following steps: Introducing at least one magnetic dopant element or compound into a topological insulator material; breaking the spin symmetry of the topological insulator material through the magnetic dopant element or compound, resulting in a spin-momentum locking phenomenon on the surface of the topological insulator material; The mass parameters of the topological insulator material are adjusted, and the local magnetic state changes of the topological insulator material under different mass parameters are analyzed using Green's function. The local magnetic state changes of the topological insulator material under different mass parameters were analyzed using Green's function, including: Construct the first impurity Green function and the second impurity Green function; determine the self-consistent equation set of the impurity density of states based on the first impurity Green function and the second impurity Green function; Solving the self-consistent set of density of states equations yields the local magnetic state changes of the topological insulator material; The analysis of the local magnetic state changes of the topological insulator material under different mass parameters includes: When the mass parameter is greater than 0, the mass parameter and the expansion parameter keep their signs opposite, and the body is in a trivial insulator state. When the mass parameter is less than 0, the mass parameter and the expansion parameter have the same sign. As the mass parameter increases, the magnetization region increases slowly, and it is in the quantum anomalous Hall insulator state.

2. The method for analyzing the performance of a magnetically doped topological insulator with localized magnetic states according to claim 1, characterized in that, Constructing the first impurity Green's function includes: Introducing the Green's function: Among them, the delayed Green's function The general form, where t is time, θ(t) represents the summation of the spin indices σ and σ' of the f electron, where θ(t) refers to the step function and the delay is in units of t'. Establish the equation of motion for the Green's function: Wherein, δ(t-t') is the impulse function, obtained by differentiating the step function.<i,j> This represents the summation of nearest-neighbor atoms, where H is the Hamiltonian; Taking a Fourier transform of the above equation yields its form in energy ω space: Among them, V f It is the jump strength between impurities and atoms, where N is the total number of lattice points; ε σ =ε0+Un -σ Given U, n is the local electron energy. -σ The occupancy number is the number of impurities with spin -σ, ε0 is the excitation energy of the lowest quasiparticle, and k is the wave vector.

3. The method for analyzing the performance of a magnetically doped topological insulator with localized magnetic states according to claim 2, characterized in that, Constructing the second impurity Green's function includes: Introducing a kσ , Green's function: Among them, a kσ , Atoms; Perform a Fourier transform to obtain a kσ , Expression in ω space: Where Δ is a user-defined parameter, t mn It is the jump energy between adjacent atoms. It is its conjugate complex number.

4. The method for analyzing the performance of a magnetically doped topological insulator with localized magnetic states according to claim 3, characterized in that, The self-consistent equations for the density of states of impurities are determined based on the Green's functions of the first and second impurities, including: By simultaneously establishing the Green's functions of the first and second impurities, the Green's function of the third impurity (η→0) can be determined: in, Processing the energy spectrum E of the topological insulator system yields the integral with respect to k2 and Δ: The third impurity Green's function can be derived through derivation: The density of states of the impurity is determined as follows: in: denoted by , D is the cutoff energy, U represents the correlation energy of electrons in the d orbitals of an 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 density of states; and S is the area or volume factor of the system.

5. The method for analyzing the performance of a magnetically doped topological insulator with a localized magnetic state according to claim 4, characterized in that, The fsolve algorithm is used to solve the self-consistent equations of the impurity's density of states, and the optimal number of grid points is used to obtain a solution with specific parameters.

6. The method for analyzing the performance of a magnetically doped topological insulator with localized magnetic states according to claim 1, characterized in that, Also includes: By adjusting the mass parameters, topological insulator materials can achieve quantum anomalous Hall effect or ordinary insulating state transitions in different magnetization regions.

7. A device, characterized in that, The method includes multiple processors, a memory, and a computer program stored in the memory and executable on the processors. When the multiple processors execute the computer program, they implement the method for analyzing the performance of a magnetically doped topological insulator with a localized magnetic state as described in any one of claims 1-6.

8. A storage medium, characterized in that, It stores a computer program, which, when executed, implements the 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 6.

Images