Simulation Projection Demonstration Method and Device for Isoenergetic Surfaces of Lattice Electrons under Tight-Bound Approximation

Abstract

This application relates to a method and apparatus for simulating and projecting isoenergetic surfaces of lattices under the tight-binding approximation. The method includes: constructing a stereoscopic projection device for isoenergetic surface simulation; creating a demonstration mode of the isoenergetic surface simulation on a simulation platform based on the stereoscopic projection device; drawing the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation based on the demonstration mode; and projecting and demonstrating the isoenergetic surface simulation using the stereoscopic projection device. The embodiments of this application utilize multiple lattice types, up to 14, capable of depicting a three-dimensional panorama of the isoenergetic surface, displaying dynamic processes, and showcasing the three-dimensional extended surface and two-dimensional band structure.

Description

Technical Field

[0001] This invention relates to the field of lattice electronic isoenergetic surface technology, and more specifically, to a method and apparatus for simulating and projecting lattice electronic isoenergetic surfaces under the tight-binding approximation. Background Technology

[0002] Currently, simulations and projection demonstrations of isoenergetic surfaces in crystal lattices suffer from several limitations, including a limited number of lattice types, the inability to depict a complete 3D panorama of isoenergetic surfaces, the inability to display dynamic processes, the ability to show isoenergetic surfaces at only a single lattice point, and the inability to display two-dimensional band structures. Specifically:

[0003] The isoenergetic surfaces of general crystal lattices are only represented by four types: simple cubic, body-centered cubic, face-centered cubic, and simple rhombohedral. The other ten types of isoenergetic surfaces are not represented. When faced with these ten types of isoenergetic surfaces, it is difficult for users to imagine their physical picture through direct calculation.

[0004] Some inventions only display two-dimensional periodic images and cannot depict clear three-dimensional images. Since certain lattice features can only be clearly shown in a three-dimensional state, this method cannot show the spatial distribution of isoenergetic surfaces, and users cannot truly understand the three-dimensional picture of isoenergetic surfaces.

[0005] Some isoenergetic surface image displays can only show static images and cannot show the dynamic images of the isoenergetic surface parameters (such as k-wave vector) changing gradually over time. Such static observation of the stationary state is very unfavorable for users' communication and understanding and has no practical value.

[0006] Crystal lattice points have periodicity. Existing image displays often only show the local isoenergetic surface of a single lattice point, lacking a display of the continuity and periodicity of the isoenergetic surface. Such displays make it impossible for users to grasp the isoenergetic surface of the entire crystal lattice, and there is no complete physical image.

[0007] Each crystal lattice has its own two-dimensional band structure along a high symmetry line. Some displays only show images of iso-energy surfaces, ignoring this two-dimensional band structure. This lack of an image prevents users from clearly understanding the energy distribution characteristics of the crystal lattice. Summary of the Invention

[0008] This application provides a method and apparatus for simulating and projecting isoenergetic surfaces of lattice electrons under the tight-binding approximation. To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or to define the scope of protection of these embodiments. Its sole purpose is to present some concepts in a simple form as a prelude to the detailed description that follows.

[0009] In a first aspect, embodiments of this application provide a method for simulating and projecting lattice electron isoenergetic surfaces under the tight-binding approximation, the method comprising:

[0010] Construct a stereoscopic projection device for simulating isoenergetic surfaces;

[0011] Based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform;

[0012] Based on the demonstration mode, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn.

[0013] The three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated using the stereoscopic projection device to simulate the isoenergetic surface.

[0014] Optionally, the stereoscopic projection device for simulating isoenergetic surfaces includes:

[0015] Construct a three-dimensional projection device for simulating the isoenergetic surface of a quadrangular pyramid structure;

[0016] The three-dimensional projection device of the quadrangular pyramid structure is used as the three-dimensional projection device for the simulation of the isoenergetic surface.

[0017] Optionally, the step of creating a demonstration mode of the isoenergetic surface simulation on the simulation platform based on the stereoscopic projection device includes:

[0018] The simulation platform is a three-dimensional isoenergetic surface simulation platform for electrons built using MATLAB.

[0019] The stereoscopic projection device is compatible with the demonstration mode.

[0020] Optionally, drawing the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation according to the demonstration mode includes:

[0021] Based on the control region, the drawing region, and the tight binding of solid band theory, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn.

[0022] The control area and the drawing area exist within the interface of the demonstration mode.

[0023] Optionally, the control area includes: a lattice structure selection drop-down menu, a lattice display button, an isoenergetic surface display button, a Brillouin zone button, an energy slider, an auto-play button, a rotation demonstration button, a two-dimensional projection button, a two-dimensional band structure button, and an extended surface display button.

[0024] The drawing area includes a first canvas, a second canvas, and a third canvas, wherein the first canvas alternately displays a positive space lattice and a three-dimensional isoenergetic surface; the second canvas alternately displays a two-dimensional projection map and a two-dimensional band structure; and the third canvas alternately displays a reciprocal space lattice and a three-dimensional extended surface.

[0025] Optionally, the lattice types corresponding to the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure simulated by the isoenergetic surface include:

[0026] Simple cube, body-centered cube, face-centered cube, simple hexagon, simple square, body-centered square, simple orthogonal, base-centered orthogonal, body-centered orthogonal, face-centered orthogonal, rhombus, simple monoclinic, base-centered monoclinic, and triclinic.

[0027] Optionally, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated using the stereoscopic projection device to simulate the isoenergetic surface, including:

[0028] Based on the 3D projection pattern created on the simulation platform, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated on the stereoscopic projection device.

[0029] Secondly, embodiments of this application provide a simulation projection demonstration device for lattice electron isoenergetic surfaces under the tight-binding approximation, the device comprising:

[0030] A module for building a stereoscopic projection device for simulating isoenergetic surfaces;

[0031] The demonstration mode creation module is used to create a demonstration mode of the isoenergetic surface simulation on the simulation platform based on the stereoscopic projection device.

[0032] The drawing module is used to draw the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation according to the demonstration mode.

[0033] The projection demonstration module is used to project and demonstrate the simulation of the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure through the stereoscopic projection device.

[0034] Thirdly, embodiments of this application provide a computer storage medium storing multiple instructions adapted for loading and execution of the above-described method steps by a processor.

[0035] Fourthly, embodiments of this application provide a terminal that may include: a processor and a memory; wherein the memory stores a computer program adapted to be loaded by the processor and executed by the above-described method steps.

[0036] The technical solutions provided in this application embodiment may include the following beneficial effects:

[0037] In this embodiment, the method for simulating and projecting isoenergetic surfaces of lattice electrons under the tight-binding approximation first constructs a stereoscopic projection device for isoenergetic surface simulation; then, based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform; next, based on the demonstration mode, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn; finally, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated through the stereoscopic projection device. This embodiment addresses the problems in the prior art, such as the limited number of lattice types, the inability to depict a three-dimensional panorama of isoenergetic surfaces, the inability to display dynamic processes, the display of isoenergetic surfaces with only a single lattice point, and the inability to display two-dimensional band structures. By using a stereoscopic projection device to project and demonstrate the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure, it allows for the display of multiple lattice types, up to 14, enabling the depiction of a three-dimensional panorama of isoenergetic surfaces, the display of dynamic processes, and the display of three-dimensional extended surfaces and two-dimensional band structures.

[0038] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0039] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0040] Figure 1 This is a flowchart illustrating a simulation projection demonstration method for lattice electron isoenergetic surfaces under the tight-binding approximation provided in an embodiment of this application.

[0041] Figure 2 This is a schematic diagram of the light imaging principle of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0042] Figure 3 This is a schematic diagram of the overall operation of a stereoscopic projection device for a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0043] Figure 4 This is a schematic diagram of the start interface of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0044] Figure 5 This is a schematic diagram of the "display lattice" state of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0045] Figure 6This is a schematic diagram of the "displaying isoenergetic surface" state of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0046] Figure 7 This is a schematic diagram of the Brillouin zone of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0047] Figure 8 This is a schematic diagram of the continuous change of isoenergetic surface in a lattice electron isoenergetic surface simulation projection demonstration method under tight-binding approximation provided in an embodiment of this application;

[0048] Figure 9 This is a schematic diagram of the "two-dimensional band structure" function setting of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0049] Figure 10 This is a schematic diagram of the "extended surface" display interface of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0050] Figure 11 This is a simplified schematic diagram of the change of the isoenergetic surface of a cubic lattice, illustrating a simulation projection demonstration method of the isoenergetic surface of a lattice electron under the tight-binding approximation provided in this application embodiment.

[0051] Figure 12 This is a schematic diagram of a simple cubic lattice two-dimensional band structure of a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0052] Figure 13 This is a schematic diagram of the change of the isoenergetic surface of a body-centered cubic lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0053] Figure 14 This is a schematic diagram of a two-dimensional band structure of a body-centered cubic lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0054] Figure 15 This is a schematic diagram of the change of the isoenergetic surface of a face-centered cubic lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0055] Figure 16 This is a schematic diagram of a two-dimensional band structure of a face-centered cubic lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0056] Figure 17This is a simplified schematic diagram of the hexagonal lattice isoenergetic surface variation of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in this application embodiment;

[0057] Figure 18 This is a schematic diagram of a simple hexagonal lattice two-dimensional band structure, which is a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in the embodiments of this application.

[0058] Figure 19 This is a simplified schematic diagram of the change of the isoenergetic surface of a tetragonal lattice, illustrating a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in this application embodiment.

[0059] Figure 20 This is a schematic diagram of a simple tetragonal lattice two-dimensional band structure, which is a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in the embodiments of this application.

[0060] Figure 21 This is a schematic diagram of the change of the isoenergetic surface of a body-centered tetragonal lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0061] Figure 22 This is a schematic diagram of a two-dimensional band structure of a body-centered tetragonal lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in the embodiments of this application.

[0062] Figure 23 This is a simplified schematic diagram of the orthogonal lattice isoenergetic surface transformation of a simulation projection demonstration method for lattice electron isoenergetic surfaces under the tight-binding approximation provided in this application embodiment;

[0063] Figure 24 This is a schematic diagram of a simple orthogonal lattice two-dimensional band structure of a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0064] Figure 25 This is a schematic diagram of the change of the bottom-centered orthogonal lattice isoenergetic surface in a simulation projection demonstration method of lattice electron isoenergetic surface under tight-binding approximation provided in an embodiment of this application;

[0065] Figure 26 This is a schematic diagram of a two-dimensional band structure of a lattice orthogonal lattice, which is a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0066] Figure 27 This is a schematic diagram of the change of the body-centered orthogonal lattice isoenergetic surface in a simulation projection demonstration method of lattice electron isoenergetic surface under tight-binding approximation provided in an embodiment of this application;

[0067] Figure 28This is a schematic diagram of a two-dimensional band structure of a body-centered orthogonal lattice, which is a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0068] Figure 29 This is a schematic diagram of the change of the face-centered orthogonal lattice isoenergetic surface in a simulation projection demonstration method of lattice electron isoenergetic surface under tight-binding approximation provided in an embodiment of this application;

[0069] Figure 30 This is a schematic diagram of a face-centered orthogonal lattice two-dimensional band structure of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0070] Figure 31 This is a schematic diagram of the rhombohedral lattice isoenergetic surface change in a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0071] Figure 32 This is a schematic diagram of a rhombohedral lattice two-dimensional band structure of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0072] Figure 33 This is a simplified schematic diagram of the monoclinic lattice isoenergetic surface change, illustrating a simulation projection demonstration method for lattice electron isoenergetic surfaces under the tight-binding approximation provided in this application embodiment.

[0073] Figure 34 This is a schematic diagram of a simple monoclinic lattice two-dimensional band structure, illustrating a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in this application embodiment.

[0074] Figure 35 This is a schematic diagram of the change of the bottom-centered monoclinic lattice isoenergetic surface in a simulation projection demonstration method of lattice electron isoenergetic surface under tight-binding approximation provided in an embodiment of this application;

[0075] Figure 36 This is a schematic diagram of a two-dimensional band structure of a monoclinic lattice under a tight-binding approximation for simulating and projecting lattice electron isoenergetic surfaces, provided in an embodiment of this application.

[0076] Figure 37 This is a schematic diagram of the triclinic lattice isoenergetic surface change in a simulation projection demonstration method of lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0077] Figure 38 This is a schematic diagram of a triclinic lattice two-dimensional band structure of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0078] Figure 39This is a schematic diagram of the three-dimensional extended surface of the S-state electrons in a cubic lattice, which is a simulation projection demonstration method of the lattice electron isoenergetic surface under the tight-binding approximation provided in this application embodiment.

[0079] Figure 40 This is a schematic diagram of the bottom-centered monoclinic lattice S-state electron extension surface of a simulation projection demonstration method for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application.

[0080] Figure 41 This is a schematic diagram of a simulation projection demonstration device for lattice electron isoenergetic surfaces under tight-binding approximation provided in an embodiment of this application;

[0081] Figure 42 This is a schematic diagram of a terminal provided in an embodiment of this application. Detailed Implementation

[0082] The following description and accompanying drawings fully illustrate specific embodiments of the invention to enable those skilled in the art to practice them.

[0083] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0084] In the following description, when referring to the accompanying drawings, the same numbers in different drawings denote the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of systems and methods consistent with some aspects of the invention as detailed in the appended claims.

[0085] In the description of this invention, it should be understood that the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Those skilled in the art can understand the specific meaning of these terms in this invention based on the specific circumstances. Furthermore, in the description of this invention, unless otherwise stated, "multiple" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0086] The following will be combined with the appendix Figure 1 - Appendix Figure 40 This paper provides a detailed description of a simulation projection demonstration method for lattice electron isoenergetic surfaces under the tight-binding approximation provided in the embodiments of this application.

[0087] Please see Figure 1-40 This document provides a flowchart illustrating a method for simulating and projecting isoenergetic surfaces of lattice electrons under the tight-binding approximation, as described in an embodiment of this application. Figure 1-40 As shown, the method in this application embodiment may include the following steps:

[0088] Band theory is a crucial theory in solid-state physics for studying the behavior of single electrons in crystal lattices. It provides excellent results in explaining electron motion within crystal lattices, the electrical conductivity of solids, alloy properties, and metal binding energies, yielding results that agree well with experiments. The tight-binding approximation (TBA) is a commonly used approximation method in band theory. It assumes that electrons moving near an atom are primarily influenced by the potential field of that single atom, while the effects of other atoms are considered perturbations. Based on the linear superposition of wavefunctions of isolated atoms, the TBA method can provide good approximation results and provides a theoretical foundation for the computation of higher-order models such as many-body problems and quasi-particle models. Using the TBA, the distribution of Bravais lattice electron iso-energy surfaces in the Brillouin zone in reciprocal space can be calculated, thus providing a spatial picture of the band structure.

[0089] Bravais lattices comprise 7 crystal systems and 14 lattice types, defined by basis vectors (a1, a2, a3) and their included angles α, β, and γ. This application utilizes MATLAB to build a simulation platform for three-dimensional electron isoenergetic surfaces, applying the tight-binding approximation from solid-state band theory to plot electron isoenergetic surfaces, covering the fourteen common Bravais lattices. The platform also provides the normal-space lattice structures and reciprocal-space unit cells for these fourteen lattices, supporting demonstrations of two-dimensional projections of isoenergetic surfaces, periodically extended isoenergetic surfaces, and two-dimensional band structures along high-symmetry lines. To enrich classroom presentations, a stereoscopic projection device was created, coupled with an automatic demonstration mode, for stereoscopic demonstrations of relevant physical phenomena in the classroom.

[0090] The basic principles of the embodiments of this application involve the drawing of Bravais lattices, the drawing of Brillouin zones, the drawing of two-dimensional band structures of s-states of lattices under tight-binding approximation, and the optical principles of demonstration instruments.

[0091] Drawing of Bravais lattices: There are 7 crystal systems and 14 lattice types of Bravais lattices, defined by basis vectors (a1, a2, a3) and their included angles α, β, γ.

[0092] Real crystals are mostly constructed by nesting simple crystal structures. For example, the zincblende structure of gallium nitride, a third-generation semiconductor material, is composed of nested face-centered cubic units, and the diamond structure can be regarded as being composed of nested two face-centered cubic units along a 1 / 4 displacement length of the diagonal.

[0093] Drawing the Brillouin zone: An infinite three-dimensional grid is defined by basis vectors (a1, a2, a3). V(x) represents a physical quantity at point x. Then the function V(x) = V(x + l1a1 + l2a2 + l3a3) is a three-dimensional periodic function with a period of (a1, a2, a3), where l1, l2, and l3 are a set of integer values ​​representing the linear superposition of (a1, a2, a3). Its reciprocal grid is determined by three reciprocal vectors, namely G... q =q1b1+q2b2+q3b3, G q Let q1, q2, and q3 represent a set of integer values, representing a linear superposition of (b1, b2, b3). Where:

[0094]

[0095] Using the reciprocal vector, V(x) can be expanded into a Fourier series, that is:

[0096]

[0097] Where (h1, h2, h3) are the Miller indices of the crystal planes, and the coefficients are expressed as...

[0098]

[0099] In a reciprocal lattice, take a reciprocal lattice point as the origin and construct the perpendicular bisectors of all reciprocal lattice vectors. The reciprocal lattice is divided into a series of regions by these surfaces. The closed region enclosed by the set of surfaces closest to the origin is called the first Brillouin zone, the region between the next closest polyhedron and the surface of the first Brillouin zone is called the second Brillouin zone, and so on.

[0100] Two-dimensional band structure plotting of s-states in crystal lattices under the tight-binding approximation: The tight-binding model is applied to various crystal structures. Although the tight-binding model is a single-electron model, it can provide good qualitative results in many cases. It also forms the basis for more advanced theoretical models, such as surface state calculations, applications related to many-body problems, and quasiparticle calculations. Furthermore, the tight-binding model can be combined with other models. Even if the tight-binding model itself fails due to exceeding its scope of application, the newly constructed model can still yield better results, thus greatly expanding its application scenarios.

[0101] The near-free electron approximation assumes that the atomic core has a weak effect on electrons, thus making their motion approximately free. This method primarily applies to valence electrons in metals, but not to other electrons in crystals, even the inner-shell electrons of metals. In most crystals, electrons are more bound; for example, the inner-shell electrons in metals and semiconductors are strongly bound by the atomic core. When the interatomic spacing in a crystal is large, the atomic core exerts a considerably strong binding force on the electron. Therefore, when an electron is relatively close to a particular atomic core, its motion is mainly influenced by the potential field of that atom, and its behavior is similar to that of electrons in isolated atoms.

[0102] At this point, isolated atoms can be treated as zero-order approximations, while the influence of the potential fields of other atoms can be considered as perturbations. At the lattice point R... m Electrons near m1a1 + m2a2 + m3a3 will be in a bound state. The form of surrounding R m It undergoes atomic orbital motion. The wave equation can be written as follows:

[0103]

[0104]

[0105] Where r is the atomic orbital radius, The wave function representing the i-state electron. For i-state electrons orbiting in an isolated atom, V(rR) is an eigenstate. m ) represents the atomic potential field at the lattice point, ε i Let i be the electron atomic energy level, E be the electron energy, ψ(r) be the corresponding wave function describing the electron's motion state, and U(r) be the periodic potential field. It is Planck's constant. Represents the trapezoidal operator. inside m e Indicates electron mass.

[0106] Using the perturbation approximation theory, for a given value of k, where N is the number of unit cells in the crystal, the solution for motion in a periodic field is:

[0107]

[0108] Eigenvalues ​​are:

[0109]

[0110] Where s represents the s-state electron, J(R) s (R) represents the interatomic spacing. s The orbital overlap integral of two atoms.

[0111] Taking the 1s state electron, which is the main focus of this discussion, as an example, we consider the orbital of the 1s state electron as the 1s state orbital φ1(rR) of each atom. m The linear combination of ) is used to synthesize the total electron orbitals, that is, using a series of functions in real space as a basis. This is because the translation operator and the Hamiltonian operator are known to commutate (i.e., ψ...). k The eigenstates of the translation operator are also the eigenstates of the Hamiltonian, k is the quantum number introduced to denote this series of eigenstates, and ψ k With φ1(rR) m The relationship between them is a Fourier transform. To diagonalize the Hamiltonian, a Fourier transform is performed, transforming it to the form defined by each Fourier component ψ. k We will discuss this under the representation of the basis. Here, each k in the reciprocal space corresponds to an eigenstate ψ of the Hamiltonian. k Each energy E0 corresponds to an eigenvalue E(k). Changing the energy E0 changes the value of the eigenvalue, and thus, according to the expression for E(k), we obtain the surface formed by the quantum numbers corresponding to all degenerate states at energy E0, which is the isoenergetic surface.

[0112] Under the tight-binding approximation, the overlap integral retains only the nearest-neighbor terms. Therefore, the energy band formed by the s-state atomic energy level can be written in the following form:

[0113]

[0114]

[0115]

[0116] in, Let J0 represent the conjugate wave function, and let R be an integer. s The overlapping integral when = 0, R m and R n Represent different grid points, note R s =R n -R m Then the transformation parameter ξ = rR m .

[0117] According to group theory, the set of rotational and rotational inversion symmetries of a crystal is called the crystal point group, denoted by G. For any point P within the Brillouin zone, the group G can be defined. p={g∈G|gp=p}. If the group is non-trivial, i.e., contains elements other than the identity element, then point P is called a high-symmetry point. A high-symmetry line in a crystal is defined as a path connecting high-symmetry points in reciprocal space in a specific manner. After calculating the three-dimensional band structure of a crystal under the tight-binding approximation, substituting the high-symmetry line path yields the two-dimensional band structure. This two-dimensional band structure reflects the characteristics of the three-dimensional band structure and is relatively simple to calculate, making it significant in band structure calculations.

[0118] Optical Principle of the Demonstration Instrument: The demonstration instrument of this application is based on stereoscopic projection. This technology originates from "Pepper's ghost." Pepper's ghost is an optical illusion that uses the reflection and refraction of planar materials to create an image. It has the visual characteristics of high contrast and clarity, strong perspective and spatial sense, and is widely used in the visual presentation of film and television special effects.

[0119] Using an optical material with both a refractive index and reflectivity of 50%, a pyramidal structure can be constructed. Light emitted from a screen placed at the base is refracted through the four sides of the pyramid, creating the Pepper illusion. Each side of the pyramid is an isosceles triangle or isosceles trapezoid, with the base and side forming a 45° angle. An optical principle diagram is shown below. Figure 2 As shown.

[0120] S100, a stereoscopic projection device for simulating isoenergetic surfaces, including:

[0121] Construct a three-dimensional projection device for simulating the isoenergetic surface of a quadrangular pyramid structure;

[0122] The three-dimensional projection device of the quadrangular pyramid structure is used as the three-dimensional projection device for the simulation of the isoenergetic surface.

[0123] In this embodiment, considering the need for portability in teaching, transparent acrylic sheet (PMMA, plexiglass) is selected as the cone material. Transparent acrylic sheet has excellent durability, with a light transmittance of over 92%, while ordinary glass has a light transmittance of only 80%. By attaching a semi-reflective and semi-transparent film to the surface of the transparent acrylic sheet, the requirement of 50% reflectivity and 50% transmittance can be achieved.

[0124] Considering the needs of actual teaching scenarios, the effective projection area is determined by the size of the square video window on the computer screen of the stereoscopic projection device. The effective projection area should not exceed the size of an isosceles trapezoid.

[0125] The 3D projection demonstration section features a self-built 3D projection device with a four-sided pyramid structure, and a corresponding demonstration mode has been created on the app. An overall diagram of the 3D projection device operation is shown below. Figure 3 As shown.

[0126] S200, based on the stereoscopic projection device, creating a demonstration mode of the isoenergetic surface simulation on the simulation platform, including:

[0127] The simulation platform is a three-dimensional isoenergetic surface simulation platform built using MATLAB, and the stereoscopic projection device is matched with the demonstration mode.

[0128] In this embodiment, the simulation part uses the App Designer platform in MATLAB for user interaction design. MATLAB is a powerful mathematical software whose numerical analysis and graphical computation functions can well serve the plotting of isoenergetic surfaces. Using the App Designer platform provided by MATLAB, a user-friendly interface can be easily built, i.e., a simulation platform for three-dimensional isoenergetic surfaces of electrons can be constructed.

[0129] Upon entering the program, the start screen looks like this. Figure 4 As shown. The program has a demo mode and a 3D projection mode. You can switch modes by clicking the "Switch Mode" button in the upper right corner of the interface. The default start screen is demo mode.

[0130] S300, based on the demonstration mode, draw the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation, including:

[0131] Based on the control region, the drawing region, and the tight binding of solid band theory, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn.

[0132] The main body of the demo mode interface is divided into a control area and a drawing area.

[0133] In this embodiment, the drawing area includes a first canvas, a second canvas, and a third canvas. The first canvas alternately displays a normal space lattice and a three-dimensional isoenergetic surface (i.e., a three-dimensional image); the second canvas alternately displays a two-dimensional projection image and a two-dimensional band structure; and the third canvas alternately displays a reciprocal space lattice and a three-dimensional extended surface (i.e., an extended image). The three-dimensional image portion and the extended image portion of the drawing area can be used to perform operations such as saving the image, manually adjusting the view, zooming, and highlighting / selecting data via the drawing toolbar buttons above the image.

[0134] In one possible implementation, the start screen can display the front-space lattice and the reverse-space lattice of a "simple cubic" lattice by default.

[0135] In this embodiment, the control area includes multiple buttons for user interaction. The control area includes: a dropdown menu for selecting a crystal lattice structure, a button to display the crystal lattice, a button to display isoenergetic surfaces, a Brillouin zone button, an energy slider, an auto-play button, a rotation demonstration button, a two-dimensional projection button, a two-dimensional band structure button, and a button to display extended surfaces. Specifically:

[0136] To select a lattice structure from the drop-down menu, click to select any lattice structure. The image will refresh automatically after selection, and the corresponding lattice parameters will be displayed in the text box below.

[0137] like Figure 5 As shown, the operation of the display lattice button is as follows: Click the button to display the corresponding lattice's positive space (lattice) lattice and reciprocal space (lattice) lattice. The isoenergetic surface function is unavailable when displaying the positive space lattice.

[0138] like Figure 6 As shown, the operation of the isoenergetic surface button is as follows: Click the button, the isoenergetic surface function is restored to use, and the upper left corner of the drawing area is changed from the positive space lattice to the isoenergetic surface three-dimensional image. The isoenergetic surface three-dimensional image is also called a three-dimensional isoenergetic surface or a three-dimensional image.

[0139] like Figure 7 As shown, the Brillouin zone button controls whether the simplified Brillouin zone is displayed on the isodynamic surface of the drawing area. The Brillouin zone is displayed in dark mode and not displayed in light mode.

[0140] The operation of the energy slider is as follows: dragging the slider continuously changes the energy of the isoenergetic surface, and the shape of the isoenergetic surface will change accordingly. Taking a simple cube as an example... Figure 8 It is an image with slider values ​​ranging from 3 to -3.

[0141] The auto-play button works as follows: Clicking the button will cause the energy slider to change automatically and continuously, freeing your hands to display the image. It auto-plays in dark mode and pauses in light mode; the default is paused.

[0142] To rotate the demo button: Click the button to automatically rotate the drawn isoenergetic surface graphic, providing a more vivid display of its three-dimensional structure. Automatic rotation occurs in dark mode, while rotation pauses in light mode (paused by default). Manual rotation can be performed using the 3D Rotation option in the toolbar above the image.

[0143] The operation of the 2D projection button is as follows: Clicking the button displays a 2D structural image along the projection direction. The projection direction is set using the projection vector below. For example, if the projection vector is along the z-axis and the projection plane is the XOY plane, then the projection vector is set to 001.

[0144] like Figure 9As shown, the operation of the two-dimensional band structure button is as follows: Click the button to display the two-dimensional band structure on the corresponding high symmetry line of the lattice, with a parameter adjustment box (without changing the iso-energy surface in the demonstration). Change the parameters and click the "Plot" button to display the corresponding two-dimensional band structure diagram (the "Plot" button can also refresh the lattice structure type).

[0145] like Figure 10 As shown, the operation of the "Show Extended Surface" button is as follows: Clicking the button will display the extended map of the corresponding lattice. In the dark state, the extended map is displayed, and in the light state, the extended map is not displayed, and only the reciprocal space lattice is displayed.

[0146] In addition, hovering the mouse over the button displays help information, allowing you to quickly understand its function. Alternatively, you can trigger the "Help" button in the upper right corner and then click the button you want to get help from again to bring up a help dialog box.

[0147] In this embodiment, the simulation platform renders 14 types of 3D lattice images, extended planes, and 2D band structures. The lattice types corresponding to the simulated 3D isoenergetic surfaces, 3D extended planes, and 2D band structures include: simple cubic, body-centered cubic, face-centered cubic, simple hexagonal, simple tetragonal, body-centered tetragonal, simple orthogonal, base-centered orthogonal, body-centered orthogonal, face-centered orthogonal, rhombohedral, simple monoclinic, base-centered monoclinic, and triclinic. Cubic and hexagonal lattices are the most common. The simulation images of the 14 types of 3D isoenergetic surface variations, 2D band structures, and 3D extended planes can be generated as follows: Figure 11-40 As shown.

[0148] In the embodiments of this application, in order to clearly demonstrate the changes in the three-dimensional isoenergetic surface, different energy values ​​can be used to demonstrate the three-dimensional isoenergetic surface under different energy states.

[0149] The embodiments of this application can also verify the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure plotted by the simulation platform. For example, for the three-dimensional isoenergetic surface of a cubic lattice, the isoenergetic surface variation image of a cubic lattice given in the literature can be used as a reference to verify the correctness of the simulation results; for the two-dimensional band structure of cubic and hexagonal lattices, the correctness of the simulation results is verified by comparing it with the band structure results given by Peter Hadley; comparing the three-dimensional extended surface of S-state electrons of a cubic lattice given in the literature with the three-dimensional extended surface of S-state electrons of a cubic lattice plotted by the simulation platform of this application can verify the correctness of the simulation results.

[0150] S400, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated through the stereoscopic projection device to simulate the isoenergetic surface, including:

[0151] Based on the 3D projection pattern created on the simulation platform, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated on the stereoscopic projection device.

[0152] This application proposes a tight-binding approximation model based on solid-state band theory. It utilizes the AppDesigner platform in MATLAB to build a comprehensive and application-rich simulation experimental platform for the electron's three-dimensional isoenergetic surface, significantly improving its visualization. This application is the first to achieve the visualization of electron three-dimensional isoenergetic surfaces covering fourteen Bravais lattices. By combining two-dimensional projection, the continuous process of isoenergetic surface variation with the k-wave vector, and the two-dimensional band structure with high symmetry lines, a stereoscopic projection device is used to present the isoenergetic surface directly to the viewer with a realistic three-dimensional effect, enabling its application in classroom teaching. The application of the stereoscopic projection device can also serve as a reference for the classroom stereoscopic demonstration of other physical phenomena.

[0153] In this embodiment, the lattice electron isoenergetic surface simulation projection demonstration method under the tight-binding approximation first constructs a stereoscopic projection device for isoenergetic surface simulation; then, based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform; next, based on the demonstration mode, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn; finally, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated through the stereoscopic projection device. This embodiment of the application has multiple lattice types, up to 14, capable of depicting a three-dimensional panorama of the isoenergetic surface, displaying dynamic processes, and showcasing the three-dimensional extended surface and the two-dimensional band structure.

[0154] The following are embodiments of the apparatus of the present invention, which can be used to execute embodiments of the method of the present invention. For details not disclosed in the embodiments of the apparatus of the present invention, please refer to the embodiments of the method of the present invention.

[0155] Please see Figure 41 The diagram illustrates a schematic representation of a lattice electron isoenergetic surface simulation projection demonstration device under the tight-binding approximation provided by an exemplary embodiment of the present invention. The device includes: a construction module 10, a demonstration mode creation module 20, a drawing module 30, and a projection demonstration module 40.

[0156] Module 10 is used to build a stereoscopic projection device for simulating isoenergetic surfaces;

[0157] The demonstration mode creation module 20 is used to create a demonstration mode of the isoenergetic surface simulation on the simulation platform based on the stereoscopic projection device.

[0158] The drawing module 30 is used to draw the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation according to the demonstration mode.

[0159] The projection demonstration module 40 is used to project and demonstrate the simulation of the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure through the stereoscopic projection device.

[0160] It should be noted that the lattice electron isoenergetic surface simulation projection demonstration device under the tight-binding approximation provided in the above embodiments is only illustrated by the division of the above functional modules when performing the lattice electron isoenergetic surface simulation projection demonstration method under the tight-binding approximation. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the lattice electron isoenergetic surface simulation projection demonstration device under the tight-binding approximation and the lattice electron isoenergetic surface simulation projection demonstration method embodiment provided in the above embodiments belong to the same concept, and the implementation process is detailed in the method embodiment, which will not be repeated here.

[0161] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0162] The lattice electron isoenergetic surface simulation projection demonstration device under the tight-binding approximation first constructs a stereoscopic projection device for isoenergetic surface simulation; then, based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform; next, based on the demonstration mode, the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation are drawn; finally, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated through the stereoscopic projection device. This application embodiment has multiple lattice types, up to 14, capable of depicting a three-dimensional panorama of the isoenergetic surface, displaying dynamic processes, and showcasing the three-dimensional extended surface and two-dimensional band structure.

[0163] The present invention also provides a computer-readable medium having program instructions stored thereon, which, when executed by a processor, implement the simulation projection demonstration method of lattice electron isoenergetic surfaces under the tight-binding approximation provided in the above-described method embodiments.

[0164] The present invention also provides a computer program product containing instructions that, when run on a computer, causes the computer to execute the simulation projection demonstration method of lattice electron isoenergy surface under the tight-binding approximation of the above-described method embodiments.

[0165] Please see Figure 42 This is a schematic diagram of the structure of a terminal provided in an embodiment of this application. Figure 42 As shown, terminal 1000 may include: at least one processor 1001, at least one network interface 1004, user interface 1003, memory 1005, and at least one communication bus 1002.

[0166] The communication bus 1002 is used to realize the connection and communication between these components.

[0167] The user interface 1003 may include a display screen and a camera. Optionally, the user interface 1003 may also include a standard wired interface and a wireless interface.

[0168] The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0169] The processor 1001 may include one or more processing cores. The processor 1001 connects to various parts within the electronic device 1000 using various interfaces and lines. It executes various functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 1005, and by calling data stored in the memory 1005. Optionally, the processor 1001 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 1001 may integrate one or more of the following: a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), and a modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed on the screen; and the modem handles wireless communication. It is understood that the modem may also be implemented as a separate chip without being integrated into the processor 1001.

[0170] The memory 1005 may include random access memory (RAM) or read-only memory. Optionally, the memory 1005 may include a non-transitory computer-readable storage medium. The memory 1005 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 1005 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-described method embodiments, etc.; the data storage area may store data involved in the above-described method embodiments, etc. Optionally, the memory 1005 may also be at least one storage device located remotely from the aforementioned processor 1001. Figure 42 As shown, the memory 1005, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and a simulation projection demonstration application for lattice electron isoenergy surfaces under the tight-binding approximation.

[0171] exist Figure 42 In the terminal 1000 shown, the user interface 1003 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 1001 can be used to call the simulation projection demonstration application of lattice electron isoenergy surface under tight-binding approximation stored in the memory 1005, and specifically perform the following operations:

[0172] Construct a stereoscopic projection device for simulating isoenergetic surfaces;

[0173] Based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform;

[0174] Based on the demonstration mode, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn.

[0175] The three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated using the stereoscopic projection device to simulate the isoenergetic surface.

[0176] In one embodiment, when the processor 1001 executes the stereoscopic projection device for simulating isoenergetic surfaces, it specifically performs the following operations:

[0177] Construct a three-dimensional projection device for simulating the isoenergetic surface of a quadrangular pyramid structure;

[0178] The three-dimensional projection device of the quadrangular pyramid structure is used as the three-dimensional projection device for the simulation of the isoenergetic surface.

[0179] In one embodiment, when the processor 1001 executes the demonstration mode of creating the isoenergetic surface simulation on the simulation platform based on the stereoscopic projection device, it specifically performs the following operations:

[0180] The simulation platform is a three-dimensional isoenergetic surface simulation platform for electrons built using MATLAB.

[0181] The stereoscopic projection device is compatible with the demonstration mode.

[0182] In one embodiment, when the processor 1001 executes the step of drawing the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation according to the demonstration mode, it specifically performs the following operations:

[0183] Based on the control region, the drawing region, and the tight binding of solid band theory, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn.

[0184] The control area and the drawing area exist within the interface of the demonstration mode;

[0185] The control area includes: a lattice structure selection drop-down menu, a lattice display button, an isoenergetic surface display button, a Brillouin zone button, an energy slider, an auto-play button, a rotation demonstration button, a two-dimensional projection button, a two-dimensional band structure button, and an extended surface display button.

[0186] The drawing area includes a first canvas, a second canvas, and a third canvas, wherein the first canvas alternately displays a positive space lattice and a three-dimensional isoenergetic surface; the second canvas alternately displays a two-dimensional projection map and a two-dimensional band structure; and the third canvas alternately displays a reciprocal space lattice and a three-dimensional extended surface.

[0187] The lattice types corresponding to the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure simulated by the isoenergetic surface include:

[0188] Simple cube, body-centered cube, face-centered cube, simple hexagon, simple square, body-centered square, simple orthogonal, base-centered orthogonal, body-centered orthogonal, face-centered orthogonal, rhombus, simple monoclinic, base-centered monoclinic, and triclinic.

[0189] In one embodiment, when the processor 1001 performs a projection demonstration of the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure through the stereoscopic projection device to simulate the isoenergetic surface, it specifically performs the following operations:

[0190] Based on the 3D projection pattern created on the simulation platform, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated on the stereoscopic projection device.

[0191] The method for simulating and projecting the isoenergetic surface of a lattice electron under the tight-binding approximation first constructs a stereoscopic projection device for isoenergetic surface simulation; then, based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on a simulation platform; next, based on the demonstration mode, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn; finally, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated through the stereoscopic projection device. This application embodiment has multiple lattice types, up to 14, capable of depicting a three-dimensional panorama of the isoenergetic surface, displaying dynamic processes, and showcasing the three-dimensional extended surface and the two-dimensional band structure.

[0192] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory, or random access memory, etc.

[0193] The above-disclosed embodiments are merely preferred embodiments of this application and should not be construed as limiting the scope of this application. Therefore, any equivalent variations made in accordance with the claims of this application shall still fall within the scope of this application.

Claims

1. A method for simulating and projecting isoenergetic surfaces of lattice electrons under the tight-binding approximation, characterized in that, Includes the following steps: Constructing a stereoscopic projection device for simulating isoenergetic surfaces includes: Construct a three-dimensional projection device for simulating the isoenergetic surface of a quadrangular pyramid structure; The three-dimensional projection device of the square pyramid structure is used as the three-dimensional projection device for the isoenergetic surface simulation. Based on the stereoscopic projection device, a demonstration mode of the isoenergetic surface simulation is created on the simulation platform, including: The simulation platform is a three-dimensional isoenergetic surface simulation platform for electrons built using MATLAB. The stereoscopic projection device is compatible with the demonstration mode; Based on the demonstration mode, the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation are drawn, including: Based on the control region, the drawing region, and the tight binding of solid band theory, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure of the isoenergetic surface simulation are drawn. The control area and the drawing area exist within the interface of the demonstration mode; The three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated using the stereoscopic projection device to simulate the isoenergetic surface.

2. The isoenergetic surface simulation and projection demonstration method according to claim 1, characterized in that, The control area includes: a lattice structure selection drop-down menu, a lattice display button, an isoenergetic surface display button, a Brillouin zone button, an energy slider, an auto-play button, a rotation demonstration button, a two-dimensional projection button, a two-dimensional band structure button, and a display extended surface button. The drawing area includes a first canvas, a second canvas, and a third canvas, wherein the first canvas alternately displays a positive space lattice and a three-dimensional isoenergetic surface; the second canvas alternately displays a two-dimensional projection map and a two-dimensional band structure; and the third canvas alternately displays a reciprocal space lattice and a three-dimensional extended surface.

3. The isoenergetic surface simulation and projection demonstration method according to claim 1, characterized in that, The lattice types corresponding to the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure simulated by the isoenergetic surface include: Simple cube, body-centered cube, face-centered cube, simple hexagon, simple square, body-centered square, simple orthogonal, base-centered orthogonal, body-centered orthogonal, face-centered orthogonal, rhombus, simple monoclinic, base-centered monoclinic, and triclinic.

4. The isoenergetic surface simulation and projection demonstration method according to claim 1, characterized in that, The three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated using the stereoscopic projection device to simulate the isoenergetic surface, including: Based on the 3D projection pattern created on the simulation platform, the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure are projected and demonstrated on the stereoscopic projection device.

5. A simulation projection demonstration device for lattice electron isoenergetic surfaces under the tight-binding approximation, characterized in that, include: A module for building a stereoscopic projection device for simulating isoenergetic surfaces; The demonstration mode creation module is used to create a demonstration mode of the isoenergetic surface simulation on the simulation platform based on the stereoscopic projection device. The drawing module is used to draw the three-dimensional isoenergetic surface, three-dimensional extended surface, and two-dimensional band structure of the isoenergetic surface simulation according to the demonstration mode. The projection demonstration module is used to project and demonstrate the simulation of the three-dimensional isoenergetic surface, the three-dimensional extended surface, and the two-dimensional band structure through the stereoscopic projection device.

6. A computer storage medium, characterized in that, The computer storage medium stores a plurality of instructions adapted for loading by a processor and executing the method steps as claimed in any one of claims 1-4.

7. A terminal, characterized in that, include: A processor and a memory; wherein the memory stores a computer program adapted to be loaded by the processor and to execute the method steps as claimed in any one of claims 1-4.

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