Method and system for simulating scanning tunnel microspectrum

Abstract

The invention provides a method for simulating a scanning tunneling microscopy, relates to the technical field of spectroscopy analogue simulation, and is used for accurately simulating a differential conductivity spectrum measured by a scanning tunneling microscopy. The strong coupling effect between the tip of the scanning tunneling microscope and the surface magnetic impurities can be effectively described, especially under the condition that a near-rattan resonance effect occurs, the spin polarization characteristics can be accurately extracted through numerical solution of a quantum state and a hybridization function in an impurity model, and common unconventional conductivity spectrum characteristics in an experiment are simulated, so that the accuracy of the spin polarization characteristics is improved. According to the method, the interaction between the local spin state and the magnetic environment can be deeply understood, information related to spin can be extracted, and a theoretical basis is provided for the field of spintronics. Meanwhile, the method can be well compared with experimental data, the accuracy of a simulation result is ensured, and the method has a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of spectroscopy simulation, and in particular to a simulation method of scanning tunneling microscopy. Background Art

[0002] In recent years, spintronics has attracted considerable attention not only for its potential applications in quantum computing and quantum information storage, but also for its close relationship to multi-electron effects in various molecular devices. This is of great significance in physics, and both experimental and theoretical research remains to be investigated and explored in depth. Scanning tunneling microscopy has proven to be a powerful tool to detect and manipulate the spin degrees of freedom of molecular systems. In such experiments, magnetic molecules with transition metal (TM) atoms are typically adsorbed on a metal substrate. By varying the distance between the scanning tunneling microscopy tip and the substrate and applying an electric and / or magnetic field, precise control over the molecular spintronic properties can be achieved.

[0003] Due to the strong correlation between the d electrons of transition metal atoms and the conduction electrons of the metal STM probe tip / substrate, Kondo states can emerge at the probe tip / molecule / substrate interface. The Kondo effect has been extensively studied in STM experiments and theoretical simulations, where differential conductance spectra are measured, revealing a sharp Kondo resonance peak at zero bias when the ambient background temperature is below the characteristic Kondo temperature. However, most of these experimental and theoretical studies have been conducted with nonmagnetic STM probes and substrates, and with weak coupling between the probe and the surface-adsorbed molecules. Over the past three decades, spin-polarized STM probes with magnetic properties have been developed and applied to scan magnetic single atoms and molecules and their environments with unprecedented spatial, spectral, and energy resolution.

[0004] In the prior art, for example, Chinese patent application No. 202410408330.8 discloses a method and system for constructing a surface atomic model based on a scanning tunneling microscope image. The shortcoming of this patent is that it focuses on the construction of non-magnetic probes and surface atomic models, and does not involve the strong coupling between spin-polarized probes and magnetic impurities, especially the electron transport characteristics under the Kondo resonance effect. Summary of the Invention

[0005] The present invention provides a scanning tunneling microscopy spectrum theoretical simulation method to solve the problem of how to accurately estimate the scanning tunneling microscopy spectrum of a given system.

[0006] In order to solve the above problems, this specification proposes a method for simulating scanning tunneling microscopy, comprising the following steps:

[0007] S1: Construct a structural model based on the system scanned by a simulated spin-polarized scanning tunneling microscope;

[0008] S2: performing first-principles calculations on the structural model to obtain geometric evolution data and electronic structure evolution data of the structural model;

[0009] S3: constructing a quantum impurity model based on the evolution data and extracting parameters required by the model;

[0010] S4: numerically solve the parameterized quantum impurity model using a quantum impurity model solver to obtain the current-voltage specific curve;

[0011] S5: performing a first-order derivative of the current-voltage specificity curve to obtain a scanning tunneling microscopy spectrum of the system.

[0012] Here, the present invention proposes a method for simulating scanning tunneling microscopy, which systematically captures the electron dynamics behavior under a scanning tunneling microscope through the construction of a structural model, first-principles calculations, the creation of a quantum impurity model, and data processing. The advantage of this method is that it combines first-principles calculations with quantum impurity models, which not only ensures accuracy from micro to macro, but also can obtain the tunneling microscopy spectrum of the system by processing the current-voltage characteristic curve. In this technology, the analysis of spin-polarized systems is particularly prominent, and can provide basic data support for the study of quantum properties of magnetic materials and spintronic devices. At the same time, its method based on first-order derivation simplifies the calculation process and improves the efficiency of obtaining experimental reference data, which is particularly suitable for applications in material design and research.

[0013] Preferably, the geometric evolution data in S2 includes information on dynamic changes in atomic positions, and the electronic structure evolution data includes energy band structure, state density and its local projection distribution.

[0014] Geometric evolution data can reveal the changing characteristics of the system's atomic arrangement, while electronic structure data reveals the system's quantum properties and electronic coupling behavior. By introducing the density of states and its local projected distribution, we can better analyze the system's spin-related information and local interactions with impurity states, thereby improving the predictive power of scanning tunneling microscopy experiments. This improvement helps to fully capture electronic structure data and expand the application scenarios of simulation results.

[0015] Preferably, the parameters in S3 include: coupling strength parameters, energy levels, Coulomb repulsion energy, substrate material and bandwidth of the scanning tunneling microscope tip.

[0016] The key parameters required to construct the quantum impurity model are listed here, including coupling strength, energy levels, Coulomb repulsion energy, substrate material, and scanning tunneling microscope tip bandwidth. These parameters form the core of the quantum impurity model and can accurately describe the electronic coupling behavior between the system's impurities and the host material. The coupling strength reflects the interaction strength between the impurity and its surrounding environment, the energy levels and Coulomb repulsion energy reveal the system's electronic occupation state, and the substrate material and tip bandwidth further refine the model's experimental environment conditions. By refining and clarifying the parameters, this simulation method can capture the localized electronic behavior of impurities in complex systems, improving the accuracy of experimental predictions and device design.

[0017] Preferably, the coupling strength parameter in S4 is obtained by calculating the local Cohen-Sam function, obtaining the hybrid function from the band bottom to the Fermi level, and then averaging it. The energy level, Coulomb repulsion, substrate material and bandwidth of the scanning tunneling microscope tip are calculated by density functional theory.

[0018] This paper describes a method for calculating coupling strength parameters using localized Cohen-Samm functions. By extracting the hybridization function and combining it with density functional theory to calculate other parameters, a precise method for extracting model parameters is achieved. The localized Cohen-Samm function not only quantifies the coupling between impurity electrons and the environment but also provides important information about the material's electronic dynamics near the Fermi level. Because the hybridization strength directly affects the behavior of the current-voltage characteristic curve, its calculation accuracy is crucial for the reliability of subsequent solutions. This integrated approach, combining density functional theory and localized hybridization functions, provides a highly accurate tool for studying spin-polarized systems and complex multi-impurity systems.

[0019] Preferably, by performing a second-order derivative on the current-voltage specificity curve in S4, the spin-related peaks or nonlinear features are extracted from the second-order differential conductivity spectrum, thereby obtaining the spin state information and spin polarization characteristics of the impurities in the system.

[0020] By taking the second-order derivative of the current-voltage specificity curve, spin-related spikes or nonlinear features can be extracted from the differential conductivity spectrum, further expanding the analytical capabilities of scanning tunneling microscopy. This method can reveal the spin states and spin polarization characteristics of impurities in the system and is an important tool for studying spintronic devices. Compared with the first-order derivative, the second-order derivative can more sensitively capture weak spin information and has a stronger ability to analyze the electronic structure bandwidth and correlation behavior of the system. This extension is extremely valuable for finding performance optimization points for spintronic devices or analyzing the quantum properties of magnetic materials, and it can achieve a higher level of research depth.

[0021] According to a scanning tunneling microscopy theoretical simulation method, the present invention provides a system for simulating scanning tunneling microscopy, comprising:

[0022] Data reading module;

[0023] Calculation module of local Cohen-Sam function;

[0024] Calculation module of hybrid functions.

[0025] Here, we propose a system for extracting coupling parameters from quantum impurity models. This system comprises a data reading module, a local Cohen-Sam function calculation module, and a hybridization function calculation module. This modular design optimizes the process of extracting model parameters from density functional theory results, efficiently and intelligently completing key steps in the simulation. Through collaborative work between modules, the analysis of impurity energy levels, coupling strengths, and hybridization behavior can be automated, significantly reducing manual intervention and potential errors, making the study of complex systems more convenient. The system's modular division of labor facilitates integration into existing research processes while ensuring the safety and reproducibility of quantum impurity analysis.

[0026] Preferably, the data reading module includes reading the output file of the density functional theory calculation, and reading the energy wave function and projection wave function information of each energy band.

[0027] A new data reader module has been added, allowing it to read energy and projection wave functions from density functional theory output files. This functionality enables quantum impurity models to more comprehensively analyze the electronic structure of host materials and impurities, extracting key data directly from density functional theory output without tedious data conversion. This not only improves data input efficiency but also ensures the integrity and accuracy of the extracted information. It is particularly suitable for systematic studies of multiple computational environments and complex band structures, providing strong data support for model reliability.

[0028] Preferably, the calculation module of the local Cohen-Samm function includes processing the read energy and wave function information according to the mathematical expression of the local Cohen-Samm function to obtain the local Cohen-Samm function of the selected impurity energy level.

[0029] The localized Cohen-Samm function here can provide electronic state characteristics of the impurity energy levels in the system, providing a direct means for high-precision description of the impurity electronic state. This is of great significance for studying the electrical transport behavior of strongly correlated systems or complex impurities, while also ensuring the integrity and physical basis of the quantum impurity model.

[0030] Preferably, the calculation module of the hybrid function includes taking the imaginary part of the inverse of the processed local Cohen-Sam function and outputting the result of the spectrum of the energy corresponding to its intensity value.

[0031] Hybridization functional intensity spectra are an important tool for analyzing the coupling strength between impurities and host materials. Here, we define the specific functionality of the module to ensure the accuracy of hybridization strength calculations. This is crucial for predicting the transport behavior of complex systems. It also directly reflects the coupling mechanism between impurities and host materials, providing solid theoretical support for the interpretation of actual experimental data.

[0032] The gains of the present invention mainly include:

[0033] (1) By combining density functional theory and quantum impurity models, the differential conductance spectra obtained by scanning tunneling microscopy can be simulated with high precision. This provides a reliable theoretical framework for studying spin-polarized scanning tunneling microscopy and can predict and explain the Kondo resonance characteristics and other unconventional conductance features observed in experiments.

[0034] (2) This method can accurately simulate the strong coupling between the magnetic scanning tunneling microscopy tip and surface adsorbed atoms, magnetic molecules, or other localized spin systems. Especially in the contact state, this strong coupling can significantly affect the shape and characteristics of the differential conductance spectrum. This helps to gain a deeper understanding of the influence of magnetic impurities on electron transport in spintronics, especially the formation mechanism of the Kondo effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 This is a flow chart of a scanning tunneling microscopy simulation method according to an embodiment of this specification;

[0037] Figure 2 The atomic structure model of the scanning tunneling microscope constructed in the embodiments of this specification;

[0038] Figure 3 This is the self-selected polarization scanning tunneling microscopy spectrum obtained by simulation calculation using this method in the examples of this specification;

[0039] Figure 4 This is a module diagram for extracting coupling parameters of the quantum impurity model according to the embodiment of this specification. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of this specification to clearly and completely describe the technical solutions in the embodiments of this specification. Obviously, the embodiments described are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this specification.

[0041] Example 1:

[0042] like Figure 1 As shown, the scanning tunneling microscopy simulation method includes the following specific implementation steps.

[0043] Step 1: According to the actual spin-polarized scanning tunneling microscope scanning system to be simulated, a structural model of the actual system needs to be constructed.

[0044] like Figure 2 As shown, this embodiment simulates the actual spin-polarized STM scanning process by modeling the STM experimental system. First, a surface model of the metal sample to be tested is constructed. A flat plate model is used to represent the idealized structure of the metal surface, and the STM tip is simplified to a cluster model. The electronic structure of the STM tip is described by the cluster model, which includes the influence of the core atoms and their external electron cloud to simplify the calculation without affecting the core physical characteristics.

[0045] Step 2: Use density functional theory to perform first-principles calculations on the constructed structural model.

[0046] Density functional theory calculations are used to determine the system's geometric structure, the positions and relative arrangements of atoms and molecules within it, and the system's electronic structure, yielding the band structure, density of states, and projected density of states. By analyzing the changes in local structure during scanning tunneling microscopy, the local geometric changes that influence electron transport are determined.

[0047] Step 3: Construct a quantum impurity model and extract the parameters required by the model.

[0048] A quantum impurity model of the system is calculated based on the geometric structure evolution data and the electronic structure evolution data. This model describes the electronic structure of impurities on the surface of the metal sample and the interaction between the impurities and their surrounding environment.

[0049] The key parameters required include the energy levels of each particle in the impurity system, the coupling strength between the impurities and the surrounding environment, the Coulomb repulsion energy between electrons, the properties of the substrate material and the bandwidth of the scanning tunneling microscope tip. Among them, by solving the Cohen-Sam equation, the energy eigenvalues of the system are obtained. These eigenvalues correspond to the energy levels of each particle in the impurity system. By calculating the local Cohen-Sam equation, the energy distribution of the hybrid function from the band bottom to the Fermi level is obtained. The coupling strength is obtained after averaging. The interaction energy between electrons is calculated to obtain the Coulomb repulsion energy. The electronic structure and state density of the substrate are calculated to obtain the properties of the substrate material. The electronic structure of the scanning tunneling microscope tip and its interaction with the sample surface are calculated to obtain the bandwidth value.

[0050] Step 4: Numerically solve the parameterized quantum impurity model using a quantum impurity model solver to obtain the current-voltage specific curve of the system.

[0051] After all the extracted parameters are determined, these parameters are used as input to numerically solve the quantum impurity model. Here, numerical solvers such as the hierarchy of equations motion method (HEOM) and the numerical renormalization group (NRG) are used to solve the system and obtain the current-voltage specific curve. The current-voltage specific curve describes the electron transport properties of the system. The following formula is the total Hamiltonian H of the Anderson quantum impurity model that describes the electron transport properties: AIM :

[0052] H AIM =H imp +H env +H coup

[0053] Among them H imp is the Hamiltonian of the surface magnetic impurity atoms scanned by scanning tunneling microscopy, H env is the Hamiltonian of the environment, H coup is the Hamiltonian for the interaction between the environment and magnetic atomic orbitals.

[0054] Step 5: Take the first-order derivative of the current-voltage specificity curve to obtain the curve of the system's differential conductivity spectrum changing with the bias voltage, that is, the scanning tunneling microscopy spectrum.

[0055] like Figure 3As shown in the figure, the first-order derivative of the current-voltage specificity curve yields the system's differential conductance spectrum as a function of bias voltage, where z (A) represents the distance from the probe to the surface magnetic atoms, sample bias (mV) represents the bias voltage, and the color represents the intensity of the differential conductance, decreasing from red to purple. The first-order differential conductance spectrum corresponds to the scanning tunneling microscopy spectrum. By taking the second-order derivative of the current-voltage specificity curve, spin-related peaks or nonlinear features are extracted from the second-order differential conductance spectrum. The splitting width at a specific distance z in the spectrum corresponds to the energy of the magnetic atomic spin excitation, thereby obtaining the spin state information and spin polarization characteristics of the impurities in the system.

[0056] Example 2:

[0057] According to a scanning tunneling microscopy theory simulation method, the present invention provides a system for extracting coupling parameters of quantum impurity models. Figure 4 As shown, it includes the following modules:

[0058] The data reading module 210 reads the electronic state information of each atomic position from the geometric structure evolution data and electronic structure evolution data calculated by density functional theory, including the atomic local density, energy band information and wave function projection data, performs hierarchical extraction of the band structure at the atomic level, obtains the energy band density and local electronic structure of the region where the atom is located, performs weighted calculation on each energy band to extract the electron orbital information with the strongest interaction with the atom, and converts the above-mentioned read electronic state information into a mathematical model input for use by subsequent local Cohen-Sam function calculation and hybrid function calculation modules.

[0059] The local Cohen-Samm function calculation module 220 includes: calculating the projection density of the impurity energy level in the local area according to the read electronic state information, and calculating the local Cohen-Samm function based on the projection density, and providing the calculated local Cohen-Samm function result to the hybridization function calculation module as the input for hybridization strength calculation by numerically simulating the time evolution of the local Cohen-Samm function.

[0060] A hybrid function calculation module 230, wherein the hybrid function calculation module includes: calculating the hybridization strength between the impurity energy level and the conduction band in the substrate material according to the output of the local Cohen-Sam function calculation module, calculating the spectral distribution of the hybridization strength and the electronic state density, and calculating the electronic structure characteristics of the system based on the spectral distribution.

[0061] Although the process flows described above include multiple operations occurring in a particular order, it should be understood that these processes may include more or fewer operations, which may be performed sequentially or in parallel (eg, using parallel processors or a multi-threaded environment).

[0062] Those skilled in the art will appreciate that the embodiments of this specification may be provided as methods, systems, or computer program products. Therefore, the embodiments of this specification may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the embodiments of this specification may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] The foregoing is merely an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should all be included within the scope of the claims of the present application.

Claims

1. A method for simulating scanning tunneling microscopy, characterized in that: The following steps are involved: S1: Construct a structural model based on the system scanned by the simulated spin-polarized scanning tunneling microscope; S2: performing first-principles calculations on the structural model to obtain geometric evolution data and electronic structure evolution data of the structural model; S3: constructing a quantum impurity model based on the evolution data and extracting parameters required by the model; S4: numerically solve the parameterized quantum impurity model using a quantum impurity model solver to obtain the current-voltage specific curve; S5: performing a first-order derivative of the current-voltage specificity curve to obtain a scanning tunneling microscopy spectrum of the system.

2. The method for simulating scanning tunneling microscopy according to claim 1, characterized in that: The geometric evolution data described in S1 include information on the dynamic changes in atomic positions, and the electronic structure evolution data include energy band structure, state density and its local projection distribution.

3. The method for simulating scanning tunneling microscopy according to claim 1, characterized in that: The geometric evolution data described in S2 includes information on dynamic changes in atomic positions, and the electronic structure evolution data includes energy band structure, state density and its local projection distribution.

4. The method for simulating scanning tunneling microscopy according to claim 1, wherein: The parameters described in S3 include: coupling strength parameters, energy levels, Coulomb repulsion energy, substrate material and bandwidth of the scanning tunneling microscope tip.

5. The method for simulating scanning tunneling microscopy according to claim 3, characterized in that: The coupling strength parameters described in S4 are obtained by calculating the local Cohen-Sam function, obtaining the hybrid function from the band bottom to the Fermi level, and then averaging it. The energy levels, Coulomb repulsion, substrate material and bandwidth of the scanning tunneling microscope tip are calculated by density functional theory.

6. The method for simulating scanning tunneling microscopy according to claim 1, characterized in that: By taking the second-order derivative of the current-voltage specificity curve described in S4, the spin-related peaks or nonlinear features are extracted from the second-order differential conductivity spectrum, thereby obtaining the spin state information and spin polarization characteristics of the impurities in the system.

7. A system for simulating scanning tunneling microscopy, characterized in that: include: Data reading module; Calculation module of local Cohen-Sam function; Calculation module of hybrid functions.

8. The system for extracting quantum impurity model coupling parameters according to claim 6, characterized in that: The data reading module includes reading the output file of the density functional theory calculation, and reading the energy wave function and projection wave function information of each energy band.

9. The system for extracting quantum impurity model coupling parameters according to claim 6, characterized in that: The calculation module of the local Cohen-Samm function includes processing the read energy and wave function information according to the mathematical expression of the local Cohen-Samm function to obtain the local Cohen-Samm function of the selected impurity energy level.

10. The system for extracting quantum impurity model coupling parameters according to claim 6, characterized in that: The calculation module of the hybrid function includes taking the imaginary part of the inverse of the processed local Cohen-Sam function and outputting the result of the spectrum of the energy corresponding to the intensity value.

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