Method and device for realizing valley Chen number inversion in honeycomb beam lattice

Abstract

The disclosed embodiments relate to a method and apparatus for achieving valley-Chern number inversion in a honeycomb beam lattice, and relate to the field of phononic crystal technology. The method comprises: establishing a two-dimensional honeycomb beam lattice model and applying periodic boundary conditions at the model's boundaries; constructing an irreducible Brillouin zone in reciprocal space based on the periodic boundary conditions, performing energy band calculations based on the boundaries of the irreducible Brillouin zone, and determining the wave functions corresponding to the energy bands of the model; adjusting the added mass at the model nodes and the contact area of ​​the lattice, and calculating the Berry curvature corresponding to different contact areas based on the wave function; calculating the valley-Chern number corresponding to different contact areas based on the Berry curvature, and determining the inversion of the valley-Chern number. The disclosed embodiments can flexibly achieve valley-Chern number inversion in a honeycomb beam lattice without changing the scatterer or mass distribution.

Description

Technical Field

[0001] The present disclosure relates to the field of phononic crystal technology, and in particular to a method, device, computer-readable storage medium, and electronic device for achieving valley Chern number inversion in a honeycomb beam lattice. Background Art

[0002] A lattice is a repetitive structure of points arranged in an orderly manner in space, usually composed of atoms, ions, or molecules, which determines the crystal structure and other physical properties of a substance. Generally speaking, lattices can be divided into simple cubic lattices, close-packed hexagonal lattices, and face-centered cubic lattices, while honeycomb beam lattices are a common type of close-packed hexagonal lattices. In two-dimensional systems, the valley-Chern number is generally used as a topological invariant. By inverting the valley-Chern number in the two-dimensional honeycomb beam lattice and using the structure corresponding to the opposite valley-Chern number to flexibly construct the structural interface, the flexible transmission of valley topological edge states along the interface path can be achieved.

[0003] Related technologies primarily invert the Chern number by changing the mass distribution at the nodes within the honeycomb beam lattice or rotating the scatterer angles. However, this method is relatively simple and requires changing the scatterers or mass distribution, limiting the flexibility of structural design. Therefore, there is room for improvement in the flexibility of methods for inverting the Chern number in honeycomb beam lattices.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute an existing solution known to ordinary technicians in this field. Summary of the Invention

[0005] The purpose of the present disclosure is to provide a method for realizing the inversion of valley Chern number in honeycomb beam lattice, an apparatus for realizing the inversion of valley Chern number in honeycomb beam lattice, a storage medium and an electronic device, which can flexibly realize the inversion of valley Chern number in honeycomb beam lattice without changing the scatterer or mass distribution.

[0006] According to a first aspect of the present disclosure, a method for achieving inversion of the Valley-Chern number in a honeycomb beam lattice is provided, comprising: establishing a two-dimensional honeycomb beam lattice model and applying periodic boundary conditions at the boundaries of the model; constructing an irreducible Brillouin zone in reciprocal space according to the periodic boundary conditions, and performing energy band calculations based on the boundaries of the irreducible Brillouin zone to determine the wave functions corresponding to the energy bands of the model; adjusting the added mass at the model nodes and the contact area of ​​the lattice, and obtaining the Berry curvature corresponding to different contact areas according to the wave function calculation; obtaining the Valley-Chern number corresponding to different contact areas according to the Berry curvature calculation, and determining the inversion of the Valley-Chern number.

[0007] In some exemplary embodiments of the present disclosure, based on the aforementioned technical solution, energy band calculations are performed based on the boundaries of the irreducible Brillouin zone to determine the wave functions corresponding to the energy bands of the model, including: dividing the boundaries of the irreducible Brillouin zone, and sweeping and performing energy band calculations on the dividing points to determine the band gap characteristics corresponding to the model; and determining the wave functions corresponding to the energy bands of the model based on the band gap characteristics.

[0008] In some exemplary embodiments of the present disclosure, based on the aforementioned technical solution, the band gap characteristics of the model are determined, including: using the in-plane and out-of-plane polarization formula to screen the band gap characteristics to obtain the out-of-plane band gap characteristics corresponding to the model; and verifying the out-of-plane band gap characteristics corresponding to the model through numerical and simulation calculation comparison.

[0009] In some exemplary embodiments of the present disclosure, based on the aforementioned technical solution, the contact area between the added mass at the model node and the lattice is adjusted, and the Berry curvature corresponding to different contact areas is obtained according to the wave function calculation, including: adjusting the radius of the added mass at the model node to change the contact area between the added mass and the lattice; substituting the wave function into the calculation formula of the Berry curvature to obtain the Berry curvature corresponding to different contact areas.

[0010] In some exemplary embodiments of the present disclosure, the additional mass includes an upper cylinder, an intermediate cylinder, and a lower cylinder. Based on the aforementioned technical solution, the radius of the additional mass at the model node is adjusted, including: fixing the radius of the intermediate cylinder of the additional mass, and making the same adjustment to the radii of the upper cylinder and the lower cylinder.

[0011] In some exemplary embodiments of the present disclosure, based on the aforementioned technical solution, the Valley-Chen numbers corresponding to different contact areas are calculated according to the Berry curvature, and the reversal of the Valley-Chen numbers is determined, including: integrating the Berry curvature corresponding to the adjacent area of ​​the high symmetric corner point in the irreducible Brillouin zone to obtain the Valley-Chen numbers corresponding to different contact areas and establishing a change curve of the Valley-Chen numbers; if the value of the Valley-Chen number in the change curve is reversed, the Valley-Chen number corresponding to the honeycomb beam lattice is reversed.

[0012] In some exemplary embodiments of the present disclosure, the method for achieving valley-Chern number inversion in a honeycomb beam lattice further includes: determining a radius critical value corresponding to the additional mass at which valley-Chern number inversion occurs; obtaining the band structure and Berry curvature distribution corresponding to the honeycomb beam lattice when the radius of the additional mass is on both sides of the radius critical value; and verifying the inversion of the valley-Chern number based on the band structure and Berry curvature distribution.

[0013] According to a second aspect of the present disclosure, a device for realizing the inversion of the Valley-Chern number in a honeycomb beam lattice is provided, comprising: a boundary condition applying module, which can be used to establish a two-dimensional honeycomb beam lattice model and apply periodic boundary conditions at the boundaries of the model; a wave function determining module, which can be used to construct an irreducible Brillouin zone in the reciprocal space according to the periodic boundary conditions, and perform energy band calculation based on the boundaries of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model; a Berry curvature calculating module, which can be used to adjust the added mass at the model node and the contact area of ​​the lattice, and obtain the Berry curvature corresponding to different contact areas according to the wave function calculation; and a Valley-Chern number inversion module, which can be used to obtain the Valley-Chern number corresponding to different contact areas according to the Berry curvature calculation, and determine the inversion of the Valley-Chern number.

[0014] According to a third aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for realizing valley Chern number inversion in a honeycomb beam lattice according to the first aspect and its possible implementation methods are implemented.

[0015] According to a fourth aspect of the present disclosure, an electronic device is provided, comprising: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute the method for realizing valley Chern number inversion in a honeycomb beam lattice of the above-mentioned first aspect and its possible implementation manner by executing the executable instructions.

[0016] In the technical solution provided by the embodiments of the present disclosure, periodic boundary conditions are applied at the boundaries of a two-dimensional honeycomb beam lattice model to construct an irreducible Brillouin zone in reciprocal space, and energy band calculations are performed to determine the wave functions corresponding to the energy bands of the lattice model. The added mass at the model nodes and the contact area of ​​the lattice are then adjusted, and the Berry curvature corresponding to different contact areas is calculated based on the wave functions. Finally, the Valley-Chern number corresponding to different contact areas is calculated based on the Berry curvature, and the inversion of the Valley-Chern number is determined. On the one hand, by adjusting the added mass at the nodes and the contact area of ​​the lattice in the two-dimensional honeycomb beam lattice model, the Berry curvature corresponding to the lattice model can be changed, thereby changing the Valley-Chern number corresponding to the lattice model. On the other hand, by adjusting the added mass at the nodes and the contact area of ​​the lattice in the two-dimensional honeycomb beam lattice model, the Valley-Chern number inversion in the honeycomb beam lattice can be flexibly achieved without changing the scatterers or mass distribution, thereby providing conditions for the flexible transmission of valley topological edge states along interface paths.

[0017] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, are used to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0019] Figure 1 A schematic diagram shows an application scenario in which the method and apparatus for implementing valley Chern number inversion in a honeycomb beam lattice according to an embodiment of the present disclosure can be applied.

[0020] Figure 2 A schematic flow chart of a method for achieving valley Chern number inversion in a honeycomb beam lattice in an embodiment of the present disclosure is schematically shown.

[0021] Figure 3 The structural diagram of the two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is schematically shown.

[0022] Figure 4 A reference diagram schematically illustrates the irreducible Brillouin zone in an embodiment of the present disclosure.

[0023] Figure 5 A reference schematic diagram schematically illustrates the mass distribution of a unit cell node of a two-dimensional honeycomb beam lattice in an embodiment of the present disclosure.

[0024] Figure 6 A reference diagram schematically illustrates a curve of valley number variation in an embodiment of the present disclosure.

[0025] Figures 7A-7B A reference diagram schematically illustrates the energy band structure of a unit cell of a two-dimensional honeycomb beam lattice in an embodiment of the present disclosure.

[0026] Figures 8A-8B A reference diagram schematically illustrates the Berry curvature distribution of a two-dimensional honeycomb beam lattice unit cell in an embodiment of the present disclosure.

[0027] Figure 9 A block diagram of a device for achieving valley Chern number inversion in a honeycomb beam lattice according to an embodiment of the present disclosure is schematically shown.

[0028] Figure 10 A block diagram schematically illustrates an electronic device in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0029] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the present disclosure will be more comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure may be practiced while omitting one or more of the specific details, or that other methods, components, devices, steps, etc. may be employed. In other cases, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of the present disclosure.

[0030] In addition, the accompanying drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0031] Dynamic analysis of engineering structures is fundamental to structural design, high reliability, and safe operation, and is a key research area in the disciplines of dynamics and control. Vibrations in structures typically propagate through elastic waves or through the coupling of elastic waves with surrounding acoustic media (such as air and water). The manipulation of elastic waves is a core fundamental issue in structural vibration control. In recent decades, phononic crystals, engineered through the use of artificially designed periodic structures, have garnered widespread attention due to their remarkable wave propagation properties, including seismic shielding, negative refraction, energy absorption, elastic wave control, and a negative Poisson's ratio. Recently, by incorporating the concept of topological insulators from condensed matter physics into phononic crystals, topological phononic crystals have emerged. These crystals, capable of supporting high-efficiency, low-loss waveguides without backscattering, have garnered significant attention in the field of structural dynamics. By designing topological phononic crystals, elastic wave diffusion and scattering losses can be effectively avoided. By simulating the valley Hall effect to adjust the node mass or rotate the scatterer angle to break the structural spatial inversion symmetry, valley topological edge states that support transmission along the boundary can be found in the topological phononic crystal system, which can largely ignore defects such as corners, holes and disorder at the interface transmission path.

[0032] A lattice is a repetitive structure of points arranged in an orderly pattern in space, typically composed of atoms, ions, or molecules. It determines the crystal structure and other physical properties of a substance. Generally speaking, lattices can be categorized into simple cubic lattices, close-packed hexagonal lattices, and face-centered cubic lattices. Honeycomb lattices are a common type of close-packed hexagonal lattice.

[0033] By calculating the topological invariants of the unit cell in a periodic structure, it is possible to determine whether valley topological edge states exist in a topological phononic crystal. In two-dimensional systems, the valley Chern number is generally used as a topological invariant; a non-zero valley Chern number indicates the presence of valley topological edge states. In mechanical systems, the wave function of the structure is the primary parameter for calculating the valley Chern number. By inverting the valley Chern number in a two-dimensional honeycomb beam lattice and utilizing the structure corresponding to the opposite valley Chern number to flexibly construct the structural interface, the flexible transmission of valley topological edge states along the interface path is achieved.

[0034] Related technologies primarily invert the valley-Chern number by changing the mass distribution at the nodes in the honeycomb beam lattice or rotating the scatterer angles. However, this method is relatively simple and requires changing the scatterer or mass distribution, limiting the flexibility of structural design. Therefore, there is room for improvement in the flexibility of methods for inverting the valley-Chern number in honeycomb beam lattices, and it is necessary to explore other methods for reversing the valley-Chern number.

[0035] In order to solve the above technical problems, an embodiment of the present disclosure provides a method for realizing the inversion of the valley Chern number in the honeycomb beam lattice, which can be used to flexibly realize the inversion of the valley Chern number in the honeycomb beam lattice without changing the scatterer or mass distribution. Figure 1 A schematic diagram shows a system architecture of a method and apparatus for implementing valley Chern number inversion in a honeycomb beam lattice, to which an embodiment of the present disclosure can be applied.

[0036] like Figure 1 As shown, the system architecture 100 may include a terminal device 101, a network and a server 102. The network may be used as a transmission medium to provide a communication link between the terminal device and the server, and is mainly used to transmit the two-dimensional honeycomb beam lattice model to the server. The network may include various connection types, such as wired or wireless communication links or optical fiber cables. The terminal device 101 may be a variety of electronic devices, including but not limited to desktop computers, portable computers, smart phones and tablet computers. It should be understood that Figure 1 The number of terminal devices 101 and servers 102 is merely illustrative, and any number of terminal devices and servers may be provided as required. For example, the server may be a server cluster consisting of multiple servers.

[0037] For example, in an embodiment of the present disclosure, a terminal device may establish a two-dimensional honeycomb beam lattice model based on the geometric data of a solid honeycomb beam lattice, and then send the two-dimensional honeycomb beam lattice model to a server via a network. The server applies periodic boundary conditions at the boundaries of the two-dimensional honeycomb beam lattice model, and then constructs an irreducible Brillouin zone in the reciprocal space based on the periodic boundary conditions. The server performs energy band calculations based on the boundaries of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model; then, the added mass at the model node and the contact area of ​​the lattice are adjusted, and the Berry curvature corresponding to different contact areas is calculated based on the wave function; then, the Valley-Chen number corresponding to different contact areas is calculated based on the Berry curvature, and the inversion of the Valley-Chen number is determined. Finally, the band structure and Berry curvature distribution corresponding to the Valley-Chen number of the two-dimensional honeycomb beam lattice model before and after the inversion are displayed, and subsequent processing is performed.

[0038] However, it is easy for those skilled in the art to understand that the above application scenarios are only for example and are not limited to this in the present exemplary embodiment. Based on this, in the embodiment of the present disclosure, a method for achieving valley Chen number inversion in the honeycomb beam lattice is provided. Figure 2 As shown in , each step of the method for achieving valley Chern number inversion in the honeycomb beam lattice in the embodiment of the present disclosure is described in detail.

[0039] In step S210 , a two-dimensional cellular beam lattice model is established, and periodic boundary conditions are applied at the boundaries of the model.

[0040] In the disclosed embodiment, the honeycomb beam lattice is a crystal structure, also known as a hexagonal closest-packed structure, which is composed of densely packed atoms or ions. The spheres are arranged on a hexagonal dense-packed layer, and then another layer of spheres fills the concave positions of the previous layer to form a hexagonal honeycomb structure. Figure 3 The schematic diagram of the structure of a two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is shown. Figure 3 As shown, the main structure of the unit cell of the honeycomb beam lattice is composed of multiple beams, and an additional mass is set at the intersection of the beams to realize the topological phononic crystal. The upper and lower cylinders of the additional mass have a diameter of d and are fixed on the main beam.

[0041] In step S220, an irreducible Brillouin zone in the reciprocal space is constructed according to the periodic boundary conditions, and energy band calculation is performed based on the boundary of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model.

[0042] In the disclosed embodiments, an irreducible Brillouin zone in reciprocal space can be constructed based on periodic boundary conditions. The irreducible Brillouin zone is defined in reciprocal space and, for a two-dimensional lattice, is typically a two-dimensional graph that can describe the band structure and electronic behavior of the crystal. Figure 4 A reference schematic diagram of the irreducible Brillouin zone corresponding to the two-dimensional honeycomb beam lattice in the embodiment of the present disclosure is schematically shown, wherein the black area represents the irreducible Brillouin zone, and the influence of the additional mass distribution on the topological characteristics of the structure can be seen.

[0043] In the embodiment of the present disclosure, reciprocal space is a space corresponding to the direct space of the lattice, which can be used to describe the reciprocal lattice and reciprocal lattice vector of the lattice. The reciprocal space is obtained by Fourier transforming the lattice.

[0044] In some embodiments, energy band calculations are performed based on the boundaries of the irreducible Brillouin zone to determine the wave functions corresponding to the energy bands of the model, specifically including the following steps: dividing the boundaries of the irreducible Brillouin zone, and sweeping and performing energy band calculations on the dividing points to determine the band gap characteristics corresponding to the model; and determining the wave functions corresponding to the energy bands of the model based on the band gap characteristics.

[0045] In the disclosed embodiments, the band gap characteristics of the honeycomb beam lattice are determined by dividing the edge of the irreducible Brillouin zone into a sufficient number of parts and sweeping the dividing points through numerical and simulation comparisons. The band gap characteristics refer to the energy gap in the band structure of the honeycomb beam lattice, that is, the energy interval between the conduction band and the valence band.

[0046] In some embodiments, determining the band gap characteristics of a two-dimensional honeycomb beam lattice model specifically includes the following steps: screening the band gap characteristics using in-plane and out-of-plane polarization formulas to obtain the out-of-plane band gap characteristics corresponding to the model; and verifying the out-of-plane band gap characteristics corresponding to the model through numerical and simulation calculation comparisons.

[0047] Specifically, after the band gap characteristics of the honeycomb beam lattice are determined by numerical and simulation calculations, the out-of-plane band gap characteristics can be screened out by the in-plane and out-of-plane polarization formula shown in formula (1):

[0048] p=∫(|w| 2 dV) / ∫(|u| 2 +|v| 2 +|w| 2 )dV (1)

[0049] Where p is the polarization factor and (u, v, w) is the displacement field within the unit cell. If p is close to 1, the calculated mode can be considered an out-of-plane mode. Preferably, in this disclosure, the mode with p>0.9 is taken as the out-of-plane mode.

[0050] Next reference Figure 2 In step S230, the contact area between the additional mass at the model node and the lattice is adjusted, and the Berry curvature corresponding to different contact areas is calculated based on the wave function.

[0051] In the disclosed embodiments, the Berry curvature corresponding to the two-dimensional honeycomb beam lattice can be adjusted by adjusting the added mass at the model nodes and the contact area of ​​the lattice, thereby changing the corresponding Valley-Chen number of the two-dimensional honeycomb beam lattice. Berry curvature is a concept used in quantum mechanics to describe the curvature of quantum states. It describes the rate of phase change caused by the evolution of a system's quantum state in parameter space as the parameters change.

[0052] In some embodiments, the contact area between the added mass at the model node and the lattice is adjusted, and the Berry curvature corresponding to different contact areas is obtained based on the wave function calculation, which specifically includes the following steps: adjusting the radius of the added mass at the model node to change the contact area between the added mass and the lattice; substituting the wave function into the calculation formula of the Berry curvature to obtain the Berry curvature corresponding to different contact areas.

[0053] Specifically, when the radius of the additional mass at different positions in the two-dimensional honeycomb beam lattice model changes, the contact area between the additional mass and the lattice can also change accordingly. Substituting the wave functions corresponding to different contact areas into the calculation formula of the Berry curvature, the Berry curvature corresponding to different contact areas can be obtained. The Berry curvature can be expressed by formula (2):

[0054]

[0055] The inner product of different vectors k is defined as n (k)|u n (k)>=∫ V u n H (k) u n (k)dr. u n (k) represents the nth order eigenmode at k, where k = (k x ,k y ), is the wave vector in the Brillouin zone.

[0056] ​In some embodiments, the additional mass of the two-dimensional honeycomb beam lattice model may include: an upper cylinder, an intermediate cylinder, and a lower cylinder. Adjusting the radius of the additional mass at the model node can be accomplished by fixing the radius of the intermediate cylinder of the additional mass and making the same adjustment to the radii of the upper cylinder and the lower cylinder.

[0057] In some embodiments, during the numerical calculation, the radius d of the intermediate cylinder of the additional mass in / 2 remains unchanged, so when the radius of the upper and lower cylinders is greater than d in / 2, the contact area between the additional mass and the beam increases, which will affect the accuracy of the numerical calculation. Therefore, this paper considers adding the excess mass to the three nodes q adjacent to the original additional mass application point. i-1 ,q i-2 and q i-3 Therefore, the structural characteristics of the two-dimensional honeycomb beam can be described more accurately. Figure 5 , Figure 5 A schematic diagram schematically illustrates the mass distribution of a unit cell node of a two-dimensional honeycomb beam lattice according to an embodiment of the present disclosure, wherein the effective area of ​​the node is represented by r e express.

[0058] Next reference Figure 2 In step S240, the valley numbers corresponding to different contact areas are calculated according to the Berry curvature, and the reversal of the valley numbers is determined.

[0059] In the disclosed embodiment, the Valley Chern number is a physical quantity that describes the topological properties of the valley in a two-dimensional material. The Valley Chern number corresponding to different contact areas is obtained by calculating the Berry curvature, and then the reversal of the Valley Chern number can be determined through the change curve of the Valley Chern number. Figure 6 The reference diagram schematically shows the change curve of the valley number in the embodiment of the present disclosure. It can be seen that in r e =d in When / 2≈2.3mm, the valley number shows a reversal phenomenon.

[0060] In some embodiments, the valley-Chen numbers corresponding to different contact areas are calculated based on the Berry curvature, and the reversal of the valley-Chen numbers is determined, including: integrating the Berry curvature corresponding to the adjacent area of ​​the high symmetric corner point in the irreducible Brillouin zone to obtain the valley-Chen numbers corresponding to different contact areas and establishing a change curve of the valley-Chen numbers; if the value of the valley-Chen number in the change curve is reversed, the valley-Chen number corresponding to the honeycomb beam lattice is reversed.

[0061] Specifically, by integrating the Berry curvature around the high symmetric corners of the Brillouin zone using formula (3), we can obtain the Valley Chen number C: v , whose expression is:

[0062]

[0063] In some embodiments, in order to better verify the inversion of the Valley-Chern number, the method for realizing the inversion of the Valley-Chern number in the honeycomb beam lattice disclosed in the present invention may further include the following steps: determining the radius critical value corresponding to the additional mass at which the Valley-Chern number inversion occurs; obtaining the band structure and Berry curvature distribution corresponding to the honeycomb beam lattice when the radius of the additional mass is on both sides of the radius critical value; and verifying the inversion of the Valley-Chern number based on the band structure and Berry curvature distribution.

[0064] Specifically, in order to more intuitively observe the inversion of the valley Chen number and the change of the band structure, Figure 7A The two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is shown in FIG. e Reference diagram of the out-of-plane band structure when =1mm, Figure 7B The two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is shown in FIG. e =3mm. It can be seen from the reference diagram of the out-of-plane band structure that the band structure does not change much due to the unchanged added total mass. Figure 8A The two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is shown in FIG. e Reference diagram of Berry curvature distribution when =1mm, Figure 8B The two-dimensional honeycomb beam lattice unit cell in the embodiment of the present disclosure is shown in FIG. e =3mm. From the Berry curvature distribution diagram, we can see an obvious reversal phenomenon, which indicates the reversal of the valley number.

[0065] In some embodiments, in the method for realizing the inversion of the Valley Chern number in the honeycomb beam lattice disclosed in the present invention, a two-dimensional honeycomb beam lattice composed of a resin material is used for analysis, and the wave function of the energy band under the corresponding band gap is calculated and brought into the Valley Chern number calculation formula to calculate the Berry curvature. The smallest unit cell is a rhombus unit cell, which is composed of multiple beams and has additional mass at the node. Taking the calculation of the Valley Chern number for the energy band under the out-of-plane band gap as an example, first, periodic boundary conditions are applied to the boundary of the beam lattice unit cell, and the irreducible Brillouin zone boundary in the inverse space is used to calculate the band structure of the unit cell. Then, the screening method of in-plane and out-of-plane polarization is used to obtain the band gap characteristics of the out-of-plane polarized wave in the band structure. Then, by changing the distribution of the additional mass around the node, the Berry curvature is calculated under different distributions of the additional mass. Finally, the corresponding Valley Chern number value is obtained through the Berry curvature, thereby judging the change in the band gap topological properties.

[0066] In the technical solution disclosed in the above embodiment, the inversion of the Valley-Chern number is achieved by changing the contact area between the added mass at the node and the lattice. The results are verified by numerical calculation and simulation, which ensures the correctness of the Valley-Chern number inversion method, thereby realizing a new control method for the elastic wave transmission path, thereby providing a theoretical basis for the application of elastic wave filters.

[0067] In the technical solution provided by the embodiments of the present disclosure, periodic boundary conditions are applied at the boundaries of a two-dimensional honeycomb beam lattice model to construct an irreducible Brillouin zone in reciprocal space, and energy band calculations are performed to determine the wave functions corresponding to the energy bands of the lattice model. The added mass at the model nodes and the contact area of ​​the lattice are then adjusted, and the Berry curvature corresponding to different contact areas is calculated based on the wave functions. Finally, the Valley-Chern number corresponding to different contact areas is calculated based on the Berry curvature, and the inversion of the Valley-Chern number is determined. On the one hand, by adjusting the added mass at the nodes and the contact area of ​​the lattice in the two-dimensional honeycomb beam lattice model, the Berry curvature corresponding to the lattice model can be changed, thereby changing the Valley-Chern number corresponding to the lattice model. On the other hand, by adjusting the added mass at the nodes and the contact area of ​​the lattice in the two-dimensional honeycomb beam lattice model, the Valley-Chern number inversion in the honeycomb beam lattice can be flexibly achieved without changing the scatterers or mass distribution, thereby providing conditions for the flexible transmission of valley topological edge states along interface paths.

[0068] The present disclosure also provides a device for realizing valley Chen number inversion in honeycomb beam lattice, referring to Figure 9 As shown in , the apparatus 900 for implementing valley-Chern number inversion in a honeycomb beam lattice may include: a boundary condition application module 901, a wave function determination module 902, a Berry curvature calculation module 903, and a valley-Chern number inversion module 904.

[0069] The boundary condition application module 901 can be used to establish a two-dimensional honeycomb beam lattice model and apply periodic boundary conditions at the boundaries of the model; the wave function determination module 902 is used to construct an irreducible Brillouin zone in the reciprocal space based on the periodic boundary conditions, and perform energy band calculations based on the boundaries of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model; the Berry curvature calculation module 903 can be used to adjust the additional mass at the model node and the contact area of ​​the lattice, and obtain the Berry curvature corresponding to different contact areas based on the wave function calculation; the Valley-Chen number inversion module 904 can be used to obtain the Valley-Chen number corresponding to different contact areas based on the Berry curvature calculation, and determine the inversion of the Valley-Chen number.

[0070] In an exemplary embodiment of the present disclosure, energy band calculations are performed based on the boundaries of the irreducible Brillouin zone to determine the wave functions corresponding to the energy bands of the model, including: dividing the boundaries of the irreducible Brillouin zone, and sweeping and performing energy band calculations on the dividing points to determine the band gap characteristics corresponding to the model; and determining the wave functions corresponding to the energy bands of the model based on the band gap characteristics.

[0071] In an exemplary embodiment of the present disclosure, determining the band gap characteristics of the model includes: screening the band gap characteristics using the in-plane and out-of-plane polarization formula to obtain the out-of-plane band gap characteristics corresponding to the model; and verifying the out-of-plane band gap characteristics corresponding to the model through numerical and simulation calculation comparison.

[0072] In an exemplary embodiment of the present disclosure, the Berry curvature calculation module is configured to: adjust the radius of the additional mass at the model node to change the contact area between the additional mass and the lattice; substitute the wave function into the calculation formula of the Berry curvature to obtain the Berry curvature corresponding to different contact areas.

[0073] In an exemplary embodiment of the present disclosure, the additional mass includes an upper cylinder, a middle cylinder and a lower cylinder, and adjusting the radius of the additional mass at the model node includes: fixing the radius of the middle cylinder of the additional mass, and making the same adjustment to the radii of the upper cylinder and the lower cylinder.

[0074] In an exemplary embodiment of the present disclosure, the Valley-Chen number inversion module is configured to: integrate the Berry curvature corresponding to the adjacent area of ​​the high symmetric corner point in the irreducible Brillouin zone, obtain the Valley-Chen number corresponding to different contact areas and establish a change curve of the Valley-Chen number; if the value of the Valley-Chen number in the change curve is reversed, the Valley-Chen number corresponding to the honeycomb beam lattice is reversed.

[0075] In an exemplary embodiment of the present disclosure, the device for realizing the inversion of the valley-Chern number in the honeycomb beam lattice also includes a valley-Chern number verification module, which is configured to: determine the radius critical value corresponding to the additional mass at which the valley-Chern number inversion occurs; obtain the band structure and Berry curvature distribution corresponding to the honeycomb beam lattice when the radius of the additional mass is on both sides of the radius critical value; and verify the inversion of the valley-Chern number based on the band structure and Berry curvature distribution.

[0076] It should be noted that the specific details of each part of the above-mentioned vulnerability detection device have been described in detail in some implementation methods of the corresponding methods. For undisclosed details, please refer to the implementation content of the method part, and thus will not be repeated here.

[0077] It should be noted that although several modules or units of the device for action execution are mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into multiple modules or units to be concretized.

[0078] Furthermore, although the steps of the method of the present disclosure are described in a particular order in the accompanying drawings, this does not require or imply that the steps must be performed in this particular order, or that all steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0079] In exemplary embodiments of the present disclosure, a computer-readable storage medium is also provided, on which is stored a program product capable of implementing the aforementioned methods of this specification. In some possible implementations, various aspects of the present disclosure may also be implemented in the form of a program product comprising program code. When the program product is executed on a terminal device, the program code is configured to cause the terminal device to execute the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of the present disclosure.

[0080] According to an embodiment of the present disclosure, a program product for implementing the above-mentioned method can be a portable compact disc read-only memory (CD-ROM) and include program code, and can be run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto. In this document, a readable storage medium can be any tangible medium containing or storing a program, which can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0081] The program product may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0082] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0083] The program code embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0084] Program code for performing the operations of the present disclosure may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, and the like, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a stand-alone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving a remote computing device, the remote computing device may be connected to the user computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0085] In an exemplary embodiment of the present disclosure, an electronic device capable of implementing the above method is also provided.

[0086] Those skilled in the art will appreciate that various aspects of the present disclosure may be implemented as systems, methods, or program products. Therefore, various aspects of the present disclosure may be implemented in the following forms: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which may be collectively referred to herein as "circuits," "modules," or "systems."

[0087] Refer to the following Figure 10 1000 according to this embodiment of the present disclosure will be described. Figure 10 The electronic device 1000 shown is merely an example and should not limit the functions and scope of use of the embodiments of the present disclosure.

[0088] like Figure 10As shown, electronic device 1000 is implemented as a general-purpose computing device. Components of electronic device 1000 may include, but are not limited to, the aforementioned at least one processing unit 1010, the aforementioned at least one storage unit 1020, a bus 1030 connecting various system components (including storage unit 1020 and processing unit 1010), and a display unit 1040.

[0089] The storage unit stores program codes, which can be executed by the processing unit 1010, so that the processing unit 1010 performs the steps according to various exemplary embodiments of the present disclosure described in the above “Exemplary Method” section of this specification. For example, the processing unit 1010 can perform the following steps: Figure 2 Follow the steps shown in .

[0090] The storage unit 1020 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 10201 and / or a cache memory unit 10202 , and may further include a read-only memory unit (ROM) 10203 .

[0091] The storage unit 1020 may also include a program / utility 10204 having a set (at least one) of program modules 10205, such program modules 10205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0092] Bus 1030 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0093] The electronic device 1000 may also communicate with one or more external devices 1100 (e.g., a keyboard, a pointing device, a Bluetooth device, etc.), one or more devices that enable a user to interact with the electronic device 1000, and / or any device that enables the electronic device 1000 to communicate with one or more other computing devices (e.g., a router, a modem, etc.). Such communication may occur via an input / output (I / O) interface 1050. Furthermore, the electronic device 1000 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network such as the Internet) via a network adapter 1060. As shown, the network adapter 1060 communicates with other modules of the electronic device 1000 via a bus 1030. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 1000, including but not limited to microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0094] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the example embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or an electronic device, etc.) to execute the method according to the embodiments of the present disclosure.

[0095] Furthermore, the above-mentioned figures are merely illustrative of the processes included in the methods according to exemplary embodiments of the present disclosure and are not intended to be limiting. It is readily understood that the processes illustrated in the above-mentioned figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0096] Other embodiments of the present disclosure will readily occur to those skilled in the art after considering the specification and practicing the inventions disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of the present disclosure that follow from the general principles of the present disclosure and include common knowledge or customary techniques in the art not invented herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the claims.

Claims

1. A method for achieving valley Chen number inversion in a honeycomb beam lattice, characterized in that: include: Establishing a two-dimensional honeycomb beam lattice model and applying periodic boundary conditions at the boundaries of the model; According to the periodic boundary conditions, an irreducible Brillouin zone in the reciprocal space is constructed, and energy band calculation is performed based on the boundary of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model; Adjusting the contact area between the additional mass at the model node and the lattice, and calculating the Berry curvature corresponding to different contact areas according to the wave function; Calculating the valley numbers corresponding to different contact areas according to the Berry curvature, and determining the reversal of the valley numbers; The adjusting of the contact area between the additional mass at the model node and the lattice, and obtaining the Berry curvature corresponding to different contact areas according to the wave function calculation, includes: Adjust the radius of the additional mass at the model node to change the contact area between the additional mass and the lattice; the additional mass includes an upper cylinder, an intermediate cylinder and a lower cylinder, and by fixing the radius of the intermediate cylinder of the additional mass, the radii of the upper cylinder and the lower cylinder are adjusted in the same way to change the contact area; wherein, when the radii of the upper and lower cylinders are greater than d in / 2, the excess mass is added to the three nodes q adjacent to the original additional mass application point. i-1 ,q i-2 and q i-3 Where, d in / 2 represents the radius of the middle cylinder of the additional mass.

2. The method for achieving valley Chen number inversion in a honeycomb beam lattice according to claim 1, characterized in that: The performing of energy band calculation based on the boundary of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model includes: Dividing the boundary of the irreducible Brillouin zone, and performing sweeping and energy band calculation on the dividing points to determine the band gap characteristics corresponding to the model; The wave function corresponding to the energy band of the model is determined according to the band gap characteristics.

3. The method for achieving valley Chen number inversion in a honeycomb beam lattice according to claim 2, characterized in that: Determining the bandgap characteristics corresponding to the model includes: The band gap characteristics are screened using an in-plane and out-of-plane polarization formula to obtain an out-of-plane band gap characteristic corresponding to the model; The out-of-plane band gap characteristics corresponding to the model are verified by comparing numerical and simulation calculations.

4. The method for achieving valley Chen number inversion in a honeycomb beam lattice according to claim 1, characterized in that: The adjusting the contact area between the additional mass at the model node and the lattice, and calculating the Berry curvature corresponding to different contact areas according to the wave function, includes: Substitute the wave function into the calculation formula of the Berry curvature to obtain the Berry curvature corresponding to different contact areas.

5. The method for achieving valley Chen number inversion in a honeycomb beam lattice according to claim 1, characterized in that: The calculating of the valley numbers corresponding to the different contact areas according to the Berry curvature and determining the reversal of the valley numbers includes: Integrating the Berry curvature corresponding to the adjacent area of ​​the high symmetric corner point in the irreducible Brillouin zone to obtain the Valley-Chen number corresponding to different contact areas and establishing a curve of the change of the Valley-Chen number; If the value of the valley number in the change curve is reversed, the valley number corresponding to the honeycomb beam lattice is reversed.

6. The method for achieving valley Chen number inversion in a honeycomb beam lattice according to claim 1, characterized in that: The method further comprises: Determining a critical radius value corresponding to the additional mass at which the inversion of the Valley Chen number occurs; Obtaining the energy band structure and Berry curvature distribution corresponding to the honeycomb beam lattice when the radius of the additional mass is on both sides of the radius critical value; The inversion of the valley-Chern number is verified based on the band structure and Berry curvature distribution.

7. A device for achieving valley number inversion in a honeycomb beam lattice, characterized in that: include: A boundary condition applying module, for establishing a two-dimensional honeycomb beam lattice model and applying periodic boundary conditions at the boundaries of the model; a wave function determination module, configured to construct an irreducible Brillouin zone in the reciprocal space according to the periodic boundary conditions, and perform energy band calculation based on the boundaries of the irreducible Brillouin zone to determine the wave function corresponding to the energy band of the model; a Berry curvature calculation module, configured to adjust the contact area between the additional mass at the model node and the lattice, and calculate the Berry curvature corresponding to different contact areas according to the wave function; A valley number reversal module, configured to calculate the valley numbers corresponding to different contact areas according to the Berry curvature and determine the reversal of the valley numbers; The adjusting of the contact area between the additional mass at the model node and the lattice, and obtaining the Berry curvature corresponding to different contact areas according to the wave function calculation, includes: Adjust the radius of the additional mass at the model node to change the contact area between the additional mass and the lattice; the additional mass includes an upper cylinder, an intermediate cylinder and a lower cylinder, and by fixing the radius of the intermediate cylinder of the additional mass, the radii of the upper cylinder and the lower cylinder are adjusted in the same way to change the contact area; wherein, when the radii of the upper and lower cylinders are greater than d in / 2, the excess mass is added to the three nodes q adjacent to the original additional mass application point. i-1 ,q i-2 and q i-3 Where, d in / 2 represents the radius of the middle cylinder of the additional mass.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for realizing valley Chern number inversion in a honeycomb beam lattice according to any one of claims 1 to 6 is realized.

9. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the method for achieving valley Chern number inversion in a honeycomb beam lattice according to any one of claims 1 to 6 by executing the executable instructions.

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