Method for predicting electronic and topological properties of two-dimensional magnetic material TiN8
By combining density functional theory and Wannier function, the problems of high prediction cost and low accuracy of new magnetic topological materials were solved, and accurate prediction of the electronic and topological properties of TiN8 materials was achieved, providing theoretical support for experimental preparation and device construction.
Patent Information
- Application Number
- CN202510743926.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-05
- Publication Date
- 2025-09-19
AI Technical Summary
The existing technology for preparing and predicting new magnetic topological materials has the problems of high cost and poor experimental precision, making it difficult to accurately predict the electronic and topological properties of two-dimensional magnetic materials.
First-principles calculations of density functional theory combined with the maximum localized Wannier function were performed using VASP, Phonopy, Wannier90 and WannierTools software. Through structural optimization, dynamic and thermodynamic stability verification, the magnetic moment direction and spin-orbit coupling were calculated, and the Wannier function was constructed to predict the electronic and topological properties of TiN8.
It has achieved accurate prediction of the electronic and topological properties of TiN8 materials, simplified the research process, reduced costs, achieved atomic-scale accuracy, and provided a theoretical basis for subsequent experimental preparation and device construction.
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Figure CN120673932A_ABST
Abstract
Description
Technical Field
[0001] The present invention is a method for predicting the electronic and topological properties of a two-dimensional magnetic material TiN8, belonging to the field of materials science (solid state physics). Specifically, it relates to a method for predicting the electronic and topological properties of materials using first principles calculations and maximum localized Wannier functions. Background Art
[0002] Topological insulators are characterized by dissipative conducting surface states and insulating bulk states, properties protected by time reversal symmetry. These materials have attracted widespread attention in condensed matter physics and materials science due to their potential to advance fundamental research and potentially enable next-generation spintronic devices. Further exploration of new two-dimensional magnetic materials with topological properties remains crucial. However, current experimental efforts to prepare and predict novel topological magnetic materials are plagued by high costs and poor experimental precision. Summary of the Invention
[0003] To address these challenges, the present invention provides a method for predicting the electronic and topological properties of the two-dimensional magnetic material TiN8. Based on first-principles physics, this method predicts a new and reliable two-dimensional magnetic topological material, TiN8, and verifies its topological properties using a physical model. This provides theoretical support for subsequent experimental preparation and device construction.
[0004] The technical problem to be solved by the present invention is achieved through the following technical solutions, including:
[0005] A method for predicting the electronic and topological properties of a two-dimensional magnetic material TiN8 is characterized by comprising the following steps:
[0006] Step 1: Based on the first-principles calculation method of density functional theory, using the VASP software package, set the magnetic parameters and perform structural optimization to obtain the stable structure of TiN8;
[0007] Step 2: Use VASP software to calculate the density functional perturbation theory (DFTP) phonon spectrum of the optimized TiN8 stable structure to verify the dynamic stability of the structure;
[0008] Step 3: The thermodynamic stability of the stable structure of TiN8 was analyzed by computational molecular dynamics simulation (AIMD) using Phonopy and VASP software packages;
[0009] Step 4: Set the magnetic calculation parameters of the VASP software package, calculate the magnetic anisotropy energy of the TiN8 material, and predict the magnetic moment direction of TiN8;
[0010] Step 5: Set the DFT+U parameters to calculate the corresponding band structure of the stable structure of TiN8 mentioned above, consider the influence of magnetism on the electronic properties of TiN8 material, calculate the band structure with spin-orbit coupling turned on, compare and analyze the electronic properties after spin-orbit coupling, and predict the electronic properties of TiN8;
[0011] Step 6: Set the parameters of the Wannier90 software package, construct the maximum localized Wannier function, draw the band diagram and fit it with the DFT band diagram to verify the reliability of the Wannier function in expressing the Hamiltonian;
[0012] Step 7: Set the WannierTools software package parameters to process the Wannier function to obtain the chiral edge states, Berry curvature of the Brillouin zone, and anomalous Hall conductance of TiN8 to predict the topological properties of the TiN8 material.
[0013] Preferably, in the above prediction method, step 1 includes:
[0014] This prediction method is based on the Kohn-Sham equation in density functional theory (DFT) in first-principles calculations. We use the Pewrdew-Burke-Ernzerhof function based on the generalized gradient approximation as the exchange-correlation functional to solve the Kohn-Sham equation; the parameters of the Brillouin zone in the KPOINTS file are 9X9X1; the plane wave cutoff energy is set to 550eV; and the interatomic force convergence criterion is set to The energy convergence value of the self-consistent field is set to 10 -5 eV; the magnetic moment parameter is set to 2μB per Ti atom based on the 3d orbital electrons outside the Ti atom.
[0015] Preferably, in the above prediction method, step 2 includes:
[0016] The dynamic stability of the molecular structure is tested for the structure that has met the convergence conditions. The existing unit cell is expanded to the original unit cell size of 3X3X1 to calculate the phonon spectrum of the density functional perturbation theory; the parameters of the Brillouin zone calculated by the VASP software are 1X1X1; the convergence standard of the force of the phonon spectrum is Considering the influence of magnetism on structural stability, the calculation parameter ISPIN=2, and a magnetic moment of 2μB is set for each Ti atom; the phonon spectrum of TiN8 is plotted, and the absence of imaginary frequency indicates that the molecular structure is kinetically stable.
[0017] Preferably, in the above prediction method, step 3 includes:
[0018] Considering the thermodynamic stability of TiN8 at room temperature, the temperature parameters of the molecular dynamics simulation of the VASP software package were set to 300K and the time was set to 2500fs; the energy-time variation graph was drawn, which showed that under 300K conditions, the structural energy tended to be stable, verifying the dynamic stability of the structure.
[0019] Preferably, in the above prediction method, step 4 includes:
[0020] The difference between the energy of the magnetic moment structure in the Z-axis direction and the magnetic moments in each direction is calculated, and it is verified that the magnetic structure in the Z-axis direction is the most stable magnetic structure.
[0021] Preferably, in the above prediction method, in step 5:
[0022] The U value of the Hubbard term in the DFT+U parameters is set to 3eV, and the J value is set to 0eV, acting on the d orbital; this indicates that turning on the spin-orbit coupling causes the material to transition from a metal to a semiconductor, and a band gap is opened at the K point.
[0023] Preferably, in the above prediction method, step 6 includes:
[0024] Atomic orbitals that contribute more near the Fermi level are selected as orbital projections for constructing the Wannier function. The atomic orbitals are the d orbitals of Ti atoms and the s and p orbitals of N atoms. The disentanglement window and the freeze window are selected according to the selected orbitals. The DFT and Wannier function bands are fitted. The Wannier bands at the Fermi level fit well with the bands calculated by the DFT method, indicating that the quality of the constructed Wannier function is sufficient to express the Hamiltonian of TiN8, and the Wannier function is simplified in the subsequent processing of the Hamiltonian compared with the DFT method.
[0025] Preferably, in the above prediction method, step 7 is:
[0026] Set the calculation parameters AHC_calc=T, SlabSS_calc=T and BerryCurvature_calc=T of the WannierTools software to calculate the anomalous Hall conductance, edge states and Berry curvature; set the occupied state energy band according to the Wannier function energy band; set the Fermi level energy; set the reciprocal space crystal plane and path of the edge state projection; set the Brillouin zone range and plane required for the Berry curvature.
[0027] Compared with the prior art, the present invention has the following beneficial effects:
[0028] The present method for predicting the electronic and topological properties of the two-dimensional magnetic material TiN8 combines first-principles calculations using density functional theory with maximally localized Wannier functions to predict the electronic and topological properties of a new type of magnetic material. This method utilizes VASP, Phonopy, Wannier90, and WannierTools software to streamline the research process. This method addresses existing issues such as inaccurate material property predictions, high prediction costs, and experimental methods that lack atomic-scale precision, providing theoretical support for subsequent experimental preparation and device construction. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] Figure 1 This is a flow chart of this embodiment;
[0030] Figure 2 The molecular structure diagram of TiN8;
[0031] Figure 3 The first molecular dynamics simulation diagram and phonon spectrum of TiN8. The left figure is the curve of structural energy changing with time under 300K conditions; the right figure is the phonon spectrum.
[0032] Figure 4 is the magnetic anisotropy energy map of TiN8;
[0033] Figure 5 The energy band diagram of TiN8 is shown on the left, without considering spin-orbit coupling, and on the right, with considering spin-orbit coupling.
[0034] Figure 6 Fit band diagrams for Wannier functions and DFT calculations;
[0035] Figure 7 is the Bailey curvature diagram of TiN8 in reciprocal space;
[0036] Figure 8 The topological properties of TiN8 predicted by the Wannier function. The left picture shows the edge state conduction channel connecting the conduction band and the valence band; the right picture shows the anomalous Hall conductance platform near the Fermi level. DETAILED DESCRIPTION
[0037] The following will combine the embodiments of the present invention and the accompanying drawings to clearly and completely describe the technical solutions and specific parameters in the embodiments of the present invention, and explain in detail the proposed method for predicting the electronic and topological properties of the two-dimensional magnetic material TiN8.
[0038] The figures in the description of the specific implementation methods serve to provide reference and explanation, and are not necessary forms of results. Tables and different graphic formats can also be used to illustrate the results in specific implementations. The figures do not limit this prediction technology solution.
[0039] The embodiment of the present invention provides a method for predicting the electronic and topological properties of the magnetic material TiN8. It mainly uses the Pewrdew-Burke-Ernzerhof function of the generalized gradient approximation as the exchange-correlation functional to solve the Kohn-Sham equation on the basis of density functional theory calculation, optimizes the structure to the convergence setting, and verifies its thermodynamic and kinetic stability. The DFT+U parameters, magnetic parameters and spin-orbit coupling parameters of the VASP software are set to calculate the band structure and magnetic properties of the stable structure of TiN8; based on the constructed maximum localized Wannier function, the contribution of specific atomic orbitals to the energy bands near the Fermi level is verified, and the maximum localized Wannier function is used to simplify the solution of the localized Hamiltonian of the material to predict the topological properties of the material. The flow chart is as follows Figure 1 shown.
[0040] Step 1: Based on the first principle calculation method of density functional theory, the VASP software package is used to optimize the structure and obtain the stable structure of TiN8 after setting the calculation conditions such as magnetic parameters. In this embodiment, the stable structure of TiN8 is as follows Figure 2 As shown, it is a central inversion symmetry system with a space group of P6 / m. It has atomic-level flatness. Each Ti atom is evenly surrounded by 6 N atoms. The bond angle ∠N-Ti-N is 60° and the Ti-N bond length is Lattice constant There are two N sites in the primitive cell that are not directly bonded to Ti, but are located around 6 bonded N atoms, with a NN bond length of The bond angle ∠NNN is 120°, forming a triangular structure. Specifically, the space group P6 / m belongs to the hexagonal crystal system. The hexagonal crystal system is characterized by a six-fold rotation axis or six-fold anti-axis, and its unit cell parameters are a = b ≠ c, α = β = 90°, and γ = 120°. Among them, "P" represents the primitive lattice (simple hexagonal lattice), "6" represents the six-fold rotation axis, and "m" represents the mirror plane.
[0041] In an optional embodiment, step 1 specifically includes: selecting the Pewrdew-Burke-Ernzerhof function based on the generalized gradient approximation as the exchange-correlation functional to solve the Kohn-Sham equation; the parameters of the Brillouin zone of the KPOINTS file are 9X9X1; the plane wave cutoff energy is set to 550eV; the interatomic force convergence standard is set to The energy convergence value of the self-consistent field is set to 10 -5 eV; the magnetic moment parameter is provided by the 3d orbital electrons outside the Ti atom and is set to 2μB per Ti atom.
[0042] Step 2: Use VASP software to calculate and simulate the density functional perturbation theory (DFTP) phonon spectrum of the optimized structure to verify the dynamic stability of the structure.
[0043] Optionally, the existing unit cell is expanded to the original unit cell size of 3X3X1 to calculate the phonon spectrum of density functional perturbation theory; the parameters of the Brillouin zone calculated by the VASP software are 1X1X1; the convergence criterion of the force of the phonon spectrum is Considering the influence of magnetism on structural stability, the calculation parameter ISPIN=2, and a magnetic moment of 2μB is set for each Ti atom. Figure 3 As shown in the figure on the right, the absence of imaginary frequencies indicates that the molecular structure is kinetically stable. Figure 3 Used to prove the stability of the structure.
[0044] Step 3: The thermodynamic stability of the structure was analyzed by computational molecular dynamics simulation (AIMD) using the Phonopy and VASP software packages.
[0045] Optionally, the temperature parameters of the molecular dynamics simulation of the VASP software package are set to 300K and the time is set to 2500fs. The energy variation curve at 300K is as follows: Figure 3 As shown in the left figure, under 300K conditions, the structural energy tends to be stable and finally converges between -1084eV and -1086eV, verifying the dynamic stability of the structure.
[0046] Step 4: Set the magnetic calculation parameters of the VASP software package, calculate the magnetic anisotropy of the material, and predict the magnetic moment direction of TiN8.
[0047] In an optional embodiment, step 4 includes the following steps: calculating the difference between the magnetic moment structure energy in the Z-axis direction and the magnetic moment in each direction, where the direction is taken as 0≤φ≤2π, 0≤θ≤π in the spherical polar coordinate system, and the value interval is 12 discrete points in φ and θ, for a total of 144 discrete points. The magnetic anisotropy energy is as follows Figure 4 As shown, in the three-dimensional coordinate system, it can be found that when the direction of the magnetic moment is in the Z-axis direction, the structural energy is the lowest and most stable, so the predicted direction of the structural magnetic moment is in the Z-axis direction.
[0048] Step 5: Set the DFT+U parameters to calculate the corresponding band structure of the above-mentioned stable magnetic structure, consider the influence of magnetism on the electronic properties of the material, calculate the band structure with spin-orbit coupling turned on, compare and analyze the electronic properties after turning on spin-orbit coupling, and predict the electronic properties of TiN8.
[0049] In an optional embodiment, step 5 includes the following steps: predicting the electronic properties of TiN8, setting the U value of the Hubbard term in the DFT+U parameter to 3 eV, setting the J value to 0 eV, and acting on the d orbital. The magnitude and direction of the Ti atomic magnetic moment are selected to be (0, 0, 2).
[0050] Step 5 in the embodiment: The band diagrams with and without spin-orbit coupling are as follows: Figure 5 The left figure shows the band diagram without spin-orbit coupling parameters enabled, while the right figure shows the band diagram with them enabled. The diagrams demonstrate that enabling spin-orbit coupling transforms the material from a metal to a semiconductor, opening a band gap at the high-symmetry K point. The dashed and solid lines in the band diagram without spin-orbit coupling parameters represent the spin-up and spin-down electron energy bands, respectively. The bands near the Fermi level are primarily contributed by the d orbitals of Ti atoms and the p orbitals of N atoms.
[0051] Step 6: Set the parameters of the Wannier90 software package, construct the maximally localized Wannier function, draw the band diagram and fit it with the DFT band diagram to verify the reliability of the Wannier function in expressing the Hamiltonian.
[0052] In an optional embodiment, step 6 includes the following steps: selecting atomic orbitals that contribute significantly near the Fermi level as orbital projections for constructing the Wannier function, the atomic orbitals being the d orbitals of Ti atoms and the s and p orbitals of N atoms; and selecting a disentanglement window and a freeze window based on the selected orbitals. The disentanglement window is between -32 eV and 5.6 eV, and the freeze window is between -32 eV and 4 eV.
[0053] In Example step 6, the DFT and Wannier function bands are fitted as follows Figure 6 As shown in the figure, the red line is the band diagram of the Wannier function, and the blue dots are the energy bands calculated by the DFT software VASP. The fitted band diagram has good overlap near the Fermi level, indicating that the constructed Wannier function is of sufficient quality to express the Hamiltonian of TiN8. In addition, the Wannier function simplifies the subsequent processing of the Hamiltonian compared to the DFT method.
[0054] Step 7: Set the parameters of the WannierTools software package to process the Wannier function to obtain the chiral edge states, Berry curvature of the Brillouin zone, and anomalous Hall conductance of TiN8 to predict the topological properties of the material.
[0055] In an optional embodiment, step 7 includes the following steps: setting the occupied state energy band according to the Wannier function energy band; setting the Fermi level energy; setting the reciprocal space crystal plane and path of the edge state projection; setting the Brillouin zone range and plane required for the Berry curvature. The calculation settings for topological properties in step 7 of the embodiment include: setting the calculation parameters AHC_calc=T, SlabSS_calc=T and BerryCurvature_calc=T of the WannierTools software to perform anomalous Hall conductance, edge state and Berry zone calculations; the above results are as follows Figure 7 and 8 As shown, the visualization of the Berry curvature shows that the integral of the Berry curvature of TiN8 in the Brillouin zone is not zero, that is, the Chern number is not zero. In the edge state diagram, there is a chiral electron conduction channel in the edge state of the material, and in the anomalous Hall conductivity diagram, there is a -1 conductivity platform that corresponds to the chiral edge state channel. The above results can predict that TiN8 is a magnetic topological insulator material with topological properties. For the above-mentioned Chern number, specifically, it is a topological invariant that represents the topological properties. Mathematically, the relationship between the Berry curvature, Chern number and anomalous Hall conductance is shown as follows:
[0056] The formula for Bailey curvature is:
[0057]
[0058] where Ω xy (k): represents the xy-plane component of the Bailey curvature in k-space. i: imaginary unit. and denote the partial derivatives with respect to momentum k and position x, respectively. represents the wave function at momentum k, α is the index of the energy band. <·|·>: represents the inner product of two wave functions.
[0059] The Chern number is the integral of the Berry curvature in the Brillouin zone:
[0060]
[0061] C stands for the Chern number, an integer that characterizes the topological properties of a system. Different Chern numbers correspond to different topological phases, and changes in the Chern number are often accompanied by topological phase transitions. is a normalization factor that ensures that the Chern number is an integer. ∫ BZ d 2 k: represents the integration of the two-dimensional wave vector k within the Brillouin zone. The Brillouin zone is the fundamental region in the crystal's momentum space, and the integral covers all possible momentum states.
[0062] The formula for anomalous Hall conductance is:
[0063]
[0064] σ xy : represents the Hall conductance, which is the component of the conductivity tensor in the x and y directions, reflecting the response of the current in the vertical direction when an electric field is applied in the material. The quantized unit of conductivity, where e is the elementary charge and h is Planck's constant, is used to quantize conductivity in the quantum Hall effect.
Claims
1. A method for predicting the electronic and topological properties of a two-dimensional magnetic material TiN8, characterized in that The steps include: Step 1: Based on the first-principles calculation method of density functional theory, using the VASP software package, set the magnetic parameters and perform structural optimization to obtain the stable structure of TiN8; Step 2: Use VASP software to calculate the density functional perturbation theory phonon spectrum of the optimized TiN8 stable structure to verify the dynamic stability of the structure; Step 3: Molecular dynamics simulations were performed using Phonopy and VASP software packages to analyze the thermodynamic stability of the stable structure of TiN8. Step 4: Set the magnetic calculation parameters of the VASP software package, calculate the magnetic anisotropy energy of the TiN8 material, and predict the magnetic moment direction of TiN8; Step 5: Set the DFT+U parameters to calculate the corresponding band structure of the stable structure of TiN8 mentioned above, consider the influence of magnetism on the electronic properties of TiN8 material, calculate the band structure with spin-orbit coupling turned on, compare and analyze the electronic properties after spin-orbit coupling, and predict the electronic properties of TiN8; Step 6: Set the parameters of the Wannier90 software package, construct the maximum localized Wannier function, draw the band diagram and fit it with the DFT band diagram to verify the reliability of the Wannier function in expressing the Hamiltonian; Step 7: Set the WannierTools software package parameters to process the Wannier function to obtain the chiral edge states, Berry curvature of the Brillouin zone, and anomalous Hall conductance of TiN8 to predict the topological properties of the TiN8 material.
2. The prediction method according to claim 1, characterized in that The step 1 comprises: This prediction method is based on the Kohn-Sham equation in density functional theory in first-principles calculations. We use the Pewrdew-Burke-Ernzerhof function based on the generalized gradient approximation as the exchange-correlation functional to solve the Kohn-Sham equation; the parameters of the Brillouin zone in the KPOINTS file are 9X9X1; the plane wave cutoff energy is set to 550eV; and the interatomic force convergence criterion is set to The energy convergence value of the self-consistent field is set to 10 -5 eV; the magnetic moment parameter is set to 2μB per Ti atom based on the 3d orbital electrons outside the Ti atom.
3. The prediction method according to claim 1, wherein: The step 2 includes: The dynamic stability of the molecular structure is tested for the structure that has met the convergence conditions. The existing unit cell is expanded to the original unit cell size of 3X3X1 to calculate the phonon spectrum of the density functional perturbation theory; the parameters of the Brillouin zone calculated by the VASP software are 1X1X1; the convergence standard of the force of the phonon spectrum is Considering the influence of magnetism on structural stability, the calculation parameter ISPIN=2, and a magnetic moment of 2μB is set for each Ti atom; the phonon spectrum of TiN8 is plotted, and the absence of imaginary frequency indicates that the molecular structure is kinetically stable.
4. The prediction method according to claim 1, wherein: The step 3 comprises: Considering the thermodynamic stability of TiN8 at room temperature, the temperature parameters of the molecular dynamics simulation of the VASP software package were set to 300K and the time was set to 2500fs; the energy-time variation graph was drawn, which showed that under 300K conditions, the structural energy tended to be stable, verifying the dynamic stability of the structure.
5. The prediction method according to claim 1, wherein: The step 4 comprises: The difference between the energy of the magnetic moment structure in the Z-axis direction and the magnetic moments in each direction is calculated, and it is verified that the magnetic structure in the Z-axis direction is the most stable magnetic structure.
6. The prediction method according to claim 1, characterized in that In step 5: The U value of the Hubbard term in the DFT+U parameters is set to 3eV, and the J value is set to 0eV, acting on the d orbital; this indicates that turning on the spin-orbit coupling causes the material to transition from a metal to a semiconductor, and a band gap is opened at the K point.
7. The prediction method according to claim 1, wherein: The step 6 comprises: Atomic orbitals that contribute more near the Fermi level are selected as orbital projections for constructing the Wannier function. The atomic orbitals are the d orbitals of Ti atoms and the s and p orbitals of N atoms. The disentanglement window and the freeze window are selected according to the selected orbitals. The DFT and Wannier function bands are fitted. The Wannier bands at the Fermi level fit well with the bands calculated by the DFT method, indicating that the quality of the constructed Wannier function is sufficient to express the Hamiltonian of TiN8, and the Wannier function is simplified in the subsequent processing of the Hamiltonian compared with the DFT method.
8. The prediction method according to claim 1, wherein: The step 7 is: setting the calculation parameters AHC_calc=T, SlabSS_calc=T and BerryCurvature_calc=T of the WannierTools software to calculate the anomalous Hall conductance, edge state and Berry curvature; setting the occupied state energy band according to the Wannier function energy band; setting the Fermi level energy; setting the reciprocal space crystal plane and path of the edge state projection; and setting the Brillouin zone range and plane required for the Berry curvature.