A two-dimensional hexagonal lattice phononic crystal and its waveguide structure

Abstract

The present invention relates to a two-dimensional hexagonal lattice phononic crystal, comprising an air plate and a resonant cavity, wherein the resonant cavity is arranged in a plurality and all are arranged on the air plate, and the bottom is connected to the air plate to form a composite primitive cell; the energy band inversion is achieved by changing the distance between the resonant cavities on one side of the air plate, thereby realizing the acoustic quantum spin Hall effect. In the above scheme, the structure is composed of an air plate-resonant cavity, which can realize the acoustic pseudospin Hall effect at a lower frequency, and the topologically protected boundary state has strong robustness to defects. At the same time, due to the existence of acoustic resonance in the air cavity, subwavelength-sized acoustic wave transmission can be realized, and the subwavelength and robust acoustic topological waveguide is conducive to the miniaturization of acoustic devices and the lossless transmission of sound waves.

Description

Technical Field

[0001] The present invention relates to the field of acoustic transmission devices, and more specifically, to a two-dimensional hexagonal lattice phononic crystal and a waveguide structure thereof. Background Art

[0002] In recent years, the discovery of quantum Hall effect (QHE), quantum spin Hall effect (QSHE) and topological insulators (TI) in condensed matter physics has aroused great research interest among scholars. Their novel topological properties provide great flexibility for manipulating robust edge states and are expected to realize unprecedented functions from spin electronics to quantum computing. Topological insulators are described by various topological invariants, such as Chern number, Z2 topological invariant, spin Chern number, valley Chern number. In topological insulators, topological transmission is topologically protected. A significant feature of topological transmission is that it has the effect of immune defects, and the original transmission state can be maintained at the location of defects with almost no reflection. The topological state in topological insulators has many novel features, such as unidirectional transmission boundary state, no backscattering, etc. The introduction of the concept of topological phase into classical wave systems, such as acoustics, optics, and mechanics, has attracted the attention of more and more scholars and provided a new direction for the development of this field.

[0003] The discovery of higher-order topological insulators has further enriched the research on topological insulators and opened up a broader research field for the research on topological insulators. In the body-edge correspondence, the dimension of the boundary state of a higher-order topological insulator of the same dimension is lower than that of the boundary state of a first-order topological insulator. For example, a two-dimensional second-order topological insulator has one-dimensional boundary states and zero-dimensional corner states, and the existence of the corner states is topologically protected, so it has strong robustness and can exist stably. In acoustic systems, pseudospin states are used to simulate the quantum spin Hall effect in electronic systems. Most of the Dirac points in pseudospin acoustic topological insulators are generated by high symmetry. Dirac points are formed by constructing a hexagonal honeycomb lattice structure of an acoustic resonant cavity with special symmetry, and then the double Dirac points are opened by changing the distance between adjacent resonant cavities, and topological inversion is achieved. In the existing technology, China's invention patent is a second harmonic control device based on high-order topological photonic crystals, including a topological corner state resonant cavity and a topological boundary state waveguide generated based on the photon spin Hall effect. The topological corner state resonant cavity and the topological boundary state waveguide are combined to obtain a two-dimensional high-order topological photonic crystal for processing the flow of nonlinear light. The invention designs a topological corner state resonant cavity based on the quantum spin Hall effect, and proves that the high localization of photons in the resonant cavity can significantly enhance the optical frequency doubling response and realize the frequency doubling signal enhanced by the corner state resonant cavity. However, this design combines the advantages of the corner state resonant cavity and the boundary state waveguide, and cannot reduce the frequency of realizing the acoustic pseudospin Hall effect, and does not enhance the robustness of the topologically protected boundary state. Summary of the invention

[0004] The present invention provides a two-dimensional hexagonal lattice phononic crystal and a waveguide structure thereof to solve the technical defects of high frequency of realizing the acoustic pseudospin Hall effect and weak robustness of the topologically protected boundary state.

[0005] In order to achieve the above invention purpose, the technical solution adopted is:

[0006] A two-dimensional hexagonal lattice phononic crystal comprises an air plate and a resonant cavity. The number of the resonant cavities is set to be several and all are arranged on the air plate. The bottom is connected to the air plate to form a composite unit cell. The energy band inversion is achieved by changing the distance between the resonant cavities on one side of the air plate, thereby realizing the acoustic quantum spin Hall effect.

[0007] In the above scheme, the structure is composed of an air plate-resonant cavity, which can realize the acoustic pseudospin Hall effect at a lower frequency. The topologically protected boundary state is highly robust to defects. At the same time, due to the existence of acoustic resonance in the air cavity, subwavelength-sized acoustic wave transmission can be achieved. The subwavelength and robust acoustic topological waveguide helps to achieve the miniaturization of acoustic devices and the lossless transmission of sound waves.

[0008] Preferably, the number of the resonant cavities is set to be an even number, and the resonant cavities are divided into two groups and are arranged on two surfaces of the air plate.

[0009] Preferably, the number of the resonant cavities is set to 12, and the 12 resonant cavities are divided into two groups and arranged on two surfaces of the air plate.

[0010] Preferably, any one of the resonant cavities is a hollow cylinder, and the bottom of the hollow cylinder is connected to the air plate.

[0011] Preferably, the surface of the air plate is a hexagon, and the centers of the six resonant cavities on each surface are on the perpendicular midline of each side of the hexagon.

[0012] Preferably, it comprises a topologically non-trivial primitive cell and a topologically trivial primitive cell; the distances between the resonant cavities on the lower surface of the air plate of the topologically non-trivial primitive cell and the topologically trivial primitive cell are the same, and the distances between the resonant cavities on the upper surface of the air plate are different.

[0013] In the above scheme, the present application designs a two-dimensional hexagonal lattice phononic crystal. The 12 identical resonant cavities distributed on the upper and lower surfaces of the air plate are used as basic units to form a composite primitive cell. The air plate at the bottom connects the scattered air cavities to form an air resonant cavity with a rigid boundary, which localizes the sound waves inside its structure. The diameter of the resonant cavity cylindrical air cavity is 2r=33.6mm, the height is H=41mm, the thickness of the air plate is h=8.2mm, the distance between each resonant cavity is R=56mm, and it is rotationally symmetric with the center of the primitive cell, showing C6 symmetry. Consider an extreme case, that is, the lattice constant a=168mm is three times the spacing R of the resonant cavities in the primitive cell, so that the distance between the resonant cavities in the primitive cell is equal to the distance between the resonant cavities between primitive cells.

[0014] COMSOL Multiphysics software based on the finite element method is used for numerical simulation. The energy band diagram of the unit cell is calculated to reflect the two-dimensional crystal properties, and periodic boundary conditions are applied to the corresponding boundaries of the unit cell. When R = a / 3, a double Dirac point appears in the center of the first Brillouin zone.

[0015] By changing the distance R between the adjacent cylindrical air cavities above the air plate, the distance (R = a / 3) between the cylindrical resonant cavities below the air plate remains unchanged. The energy band structure can be changed by changing the parameter R. The energy band inversion can be achieved by different R values.

[0016] A waveguide structure includes a plurality of two-dimensional hexagonal lattice phononic crystals.

[0017] Preferably, a finite hexagonal acoustic structure is formed by splicing a number of topological non-trivial primitive cells and a number of topological trivial primitive cells.

[0018] Preferably, the left and right sides of the finite hexagonal acoustic structure each consist of a number of topologically trivial primitive cells, and the middle portion consists of topologically non-trivial primitive cells.

[0019] Preferably, the interface between the topological non-trivial primitive cell and the topological trivial primitive cell is a curved curve, and the interface comprises a zigzag interface and a broken armchair interface.

[0020] In the above scheme, in order to verify the existence of topologically protected surface acoustic wave boundary states, the topologically trivial and non-trivial phononic crystal systems can be spliced ​​together. 20 primitive cells are selected to form a strip supercell structure, and the characteristic frequency of the strip supercell structure is calculated around 1100 Hz. Since the proposed structure can support topological boundary states, this unique property can be used to realize new functional devices.

[0021] In order to further verify the robustness of acoustic wave propagation along the sharp bend interface, defects are introduced by removing the air cavity at the interface between the topological non-trivial lattice and the topological trivial lattice (two air cavities on the front and back sides of the topological non-trivial lattice and six air cavities on the front and back sides of the topological trivial lattice are removed). Similarly, a point sound source is placed at the left port at the interface between the non-trivial unit cell and the trivial unit cell to excite at the same frequency. After the defect is introduced, the pseudospin-related boundary mode can bypass the defect in the topological waveguide, and the acoustic wave still propagates stably along the bent interface, which is basically the same as the acoustic propagation characteristics corresponding to the defect-free acoustic topological waveguide. This shows that the edge mode is almost unaffected by defect-induced backscattering. Therefore, this non-trivial edge state transmission is robust.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention provides a two-dimensional hexagonal lattice phononic crystal and a waveguide structure thereof. The structure consists of an air plate-resonance cavity, can realize the acoustic pseudospin Hall effect at a lower frequency, and the topologically protected boundary state has strong robustness to defects. At the same time, due to the existence of acoustic resonance in the air cavity, subwavelength-sized acoustic wave transmission can be realized. The subwavelength and robust acoustic topological waveguide is conducive to the miniaturization of acoustic devices and the lossless transmission of sound waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A two-dimensional hexagonal lattice phononic crystal unit cell diagram of the present invention;

[0025] Figure 2 The energy band diagram of the first Brillouin zone of the unit cell of the present invention;

[0026] Figure 3 is a first Brillouin zone diagram of the lattice of the present invention;

[0027] Figure 4 is the dispersion relation diagram of the phononic crystal unit cell (R=0.8a / 3) of the present invention;

[0028] Figure 5 is the dispersion relation diagram of the phononic crystal unit cell (R=1.1a / 3) of the present invention;

[0029] Figure 6 The eigenmode sound pressure field distribution diagram of the phononic crystal (R=0.8a / 3 and R=1.1a / 3) of the present invention at the center of the Brillouin zone;

[0030] Figure 7 Schematic diagram of a hexagonal finite acoustic structure composed of topological non-trivial phononic crystals (R=1.1a / 3) of the present invention;

[0031] Figure 8 is an eigenfrequency diagram of the hexagonal finite acoustic structure of the present invention;

[0032] Fig. 9 The sound pressure eigenfield diagrams corresponding to the body state, boundary state, and corner state of the present invention at eigenfrequencies of 1202.7 Hz, 1140.9 Hz, and 1152.1 Hz;

[0033] Fig.10 It is a schematic diagram of the strip-shaped supercell structure of the present invention;

[0034] Fig.11 is the dispersion relation diagram corresponding to the strip-shaped supercell of the present invention;

[0035] Fig.12 For the present invention Fig.11 Sound pressure field distribution diagram of point A and point B;

[0036] Fig.13 A diagram showing the structure of a two-dimensional bent acoustic waveguide spliced ​​with topologically non-trivial and topologically trivial lattices of the present invention;

[0037] Fig.14 1 is the intrinsic sound pressure field diagram of the 1-dimensional bent acoustic waveguide structure of the present invention when the excitation source frequency is 1115.9 Hz;

[0038] Fig.15 Introducing a defect map into the two-dimensional bent acoustic waveguide structure of the present invention;

[0039] Fig.16 This is a diagram of the intrinsic sound pressure field of the two-dimensional bent acoustic waveguide structure after introducing defects of the present invention at an excitation source frequency of 1115.9 Hz;

[0040] Explanation of the reference numerals: 1. air plate; 2. resonant cavity. DETAILED DESCRIPTION

[0041] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0042] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0043] Example 1

[0044] like Figure 1 As shown, a two-dimensional hexagonal lattice phononic crystal includes an air plate 1 and a resonant cavity 2. The number of the resonant cavities 2 is set to be several and all are arranged on the air plate 1. The bottom is connected to the air plate 1 to form a composite unit cell. By changing the distance between the resonant cavities 2 on one side of the air plate 1, the energy band inversion is achieved, thereby realizing the acoustic quantum spin Hall effect.

[0045] In the above scheme, the structure consists of an air plate 1-resonance cavity 2, which can realize the acoustic pseudospin Hall effect at a lower frequency. The topologically protected boundary state is highly robust to defects. At the same time, due to the existence of acoustic resonance in the air cavity, subwavelength-sized acoustic wave transmission can be achieved. The subwavelength and robust acoustic topological waveguide helps to achieve the miniaturization of acoustic devices and the lossless transmission of sound waves.

[0046] Preferably, the number of the resonant cavities 2 is set to be an even number, and the resonant cavities 2 are divided into two groups and are arranged on two surfaces of the air plate 1 .

[0047] Preferably, the number of the resonant cavities 2 is set to 12, and the 12 resonant cavities 2 are divided into two groups and arranged on two surfaces of the air plate 1.

[0048] Preferably, any one of the resonant cavities 2 is a hollow cylinder, and the bottom of the hollow cylinder is connected to the air plate 1 .

[0049] Preferably, the surface of the air plate is a hexagon, and the centers of the six resonant cavities on each surface are on the perpendicular midline of each side of the hexagon.

[0050] Preferably, it includes a topological non-trivial primitive cell and a topological trivial primitive cell; the distance between the resonant cavities 2 on the lower surface of the air plate 1 of the topological non-trivial primitive cell and the topological trivial primitive cell is the same, and the distance between the resonant cavities 2 on the upper surface of the air plate 1 is different.

[0051] Example 2

[0052] like Figure 2 to Figure 9 As shown, the present application designs a two-dimensional hexagonal lattice phononic crystal. The 12 identical resonant cavities 2 distributed on the upper and lower surfaces of the air plate 1 are used as basic units to form a composite primitive cell. The air plate 1 at the bottom connects the scattered air cavities to form an air resonant cavity with a rigid boundary, which localizes the sound waves inside its structure. The diameter of the resonant cavity cylindrical resonant cavity 2 is 2r=33.6mm, the height is H=41mm, the thickness of the air plate 1 is h=8.2mm, and the distance between each resonant cavity 2 is R=56mm, which is rotationally symmetric with the center of the primitive cell, showing C6 symmetry. Consider an extreme case, that is, the lattice constant a=168mm is three times the spacing R of the resonant cavities 2 in the primitive cell, so that the distance between the resonant cavities 2 in the primitive cell is equal to the distance between the resonant cavities 2 between the primitive cells.

[0053] COMSOL Multiphysics software based on the finite element method is used for numerical simulation. The energy band diagram of the primitive cell is calculated to reflect the two-dimensional crystal properties, and periodic boundary conditions are applied to the corresponding boundaries of the primitive cell. Figure 2As shown, when R = a / 3, a double Dirac point appears in the center of the first Brillouin zone. Figure 3 shows the first Brillouin zone of the primitive cell.

[0054] By changing the distance R between the adjacent cylindrical air cavities above the air plate, the distance (R=a / 3) between the cylindrical resonant cavities 2 below the air plate remains unchanged. The energy band structure can be changed by changing the parameter R. The energy band inversion can be achieved by different R values.

[0055] When R = 0.8a / 3, the energy band diagram of the primitive cell is as follows Figure 4 As shown. The doubly degenerate Dirac cone opens to two doubly degenerate states, and a complete band gap is generated. The green and blue dots represent the extreme points of the two frequencies at the Г point. The p state is located below the d state, showing a topologically trivial phase. When R = 1.1a / 3, the band diagram of the primitive cell is as follows Figure 5 As shown, the p state is located above the d state, and the energy band of the hexagonal lattice phononic crystal is reversed, showing a topological non-trivial phase. Figure 6 The doubly degenerate point of the primitive cell at the center of the Brillouin zone when R = 0.8a / 3 and R = 1.1a / 3 ( Figure 6 The eigenmode sound pressure field distribution corresponding to the blue and green points in the figure. From the sound pressure field distribution, it can be found that the generation of the dipole eigenstate is accompanied by the generation of the quadrupole eigenstate. The dipole state is similar to the p in the corresponding electronic system. x and p y Two symmetric modes, the quadrupole state is similar to the d xy and Two symmetric modes. Both phononic crystals have a pair of dipole and quadrupole modes, and the energy bands are reversed. At this time, since the two primitive cells (R = 0.8a / 3 and R = 1.1a / 3) only have C6 crystal symmetry, the corresponding dipole (p x ,p y ) and quadrupole (d xy , ) mode is not perfectly symmetric about the x and y axes. However, the C6 symmetry of the phononic crystal still satisfies the pseudo-time reversal operator symmetry, thus realizing the acoustic quantum spin Hall effect.

[0056] When R = 1.1a / 3, the primitive cell is a topologically non-trivial structure. Use this primitive cell to construct a finite hexagonal acoustic structure such as Figure 7 As shown, Figure 8 The eigenmode diagram of the finite hexagonal acoustic structure is shown in Figure 2. From the eigenmode diagram, we can find that there are eigenfrequencies in the complete band gap, and by observing their sound pressure eigenfields, we can find that there are one-dimensional boundary states and zero-dimensional corner states. Fig. 9The sound pressure eigenfields corresponding to the body, boundary and corner states at eigenfrequencies of 1202.7 Hz, 1140.9 Hz and 1152.1 Hz. The boundary state mode can be clearly seen from the sound pressure eigenfields. The sound pressure is mainly localized on the boundary of the hexagon, and the sound pressure intensity at other positions is almost non-existent. For the corner state mode, the sound pressure is mainly localized on the corner of the hexagon. The sound pressure eigenfield corresponding to the eigenfrequency outside the band gap is the body mode, and the sound pressure of the body mode will be distributed on the entire finite hexagonal acoustic structure.

[0057] Example 3

[0058] like Figures 10 to 16 As shown, a waveguide structure includes a plurality of two-dimensional hexagonal lattice phononic crystals.

[0059] Preferably, a finite hexagonal acoustic structure is formed by splicing a number of topological non-trivial primitive cells and a number of topological trivial primitive cells.

[0060] Preferably, the left and right sides of the finite hexagonal acoustic structure each consist of a number of topologically trivial primitive cells, and the middle portion consists of topologically non-trivial primitive cells.

[0061] Preferably, the interface between the topological non-trivial primitive cell and the topological trivial primitive cell is a curved curve, and the interface comprises a zigzag interface and a broken armchair interface.

[0062] In the above scheme, in order to verify the existence of topologically protected surface acoustic wave boundary states, the topologically trivial and non-trivial phononic crystal systems can be spliced ​​together. 20 primitive cells are selected to form a strip supercell structure, and the characteristic frequency of the strip supercell structure is calculated around 1100 Hz. Fig.10 As shown, the strip supercell structure consists of three parts. The left and right sides each consist of 5 topologically trivial primitive cells with R = 0.8a / 3, and the middle part consists of 10 topologically non-trivial primitive cells with R = 1.1a / 3. Fig.11 The band diagram of the strip supercell structure, the red and blue lines represent the boundary states, and the black area represents the body state. From the band diagram, it can be found that the boundary state spans the band gap between the upper and lower body states. Fig.12 for Fig.11 In the sound pressure field distribution diagram of points A and B, the eigenfrequencies corresponding to points A and B are the same. Fig.12It can be found that at the trivial-nontrivial boundary, the sound pressure field at point A rotates clockwise, corresponding to the downward pseudospin state; at the nontrivial-trivial boundary, the energy flow rotates counterclockwise, corresponding to the upward pseudospin state, and the sound pressure field at point A is mainly concentrated at the topological trivial and nontrivial boundary, and the energy rapidly decays in the process of propagating from the interface of two different lattices to the left and right sides. The sound pressure field distribution at point B is similar to that at point A, but the energy flow rotation direction, pseudospin direction, and propagation direction at the junction are opposite to those at point A. Therefore, there are two different pseudospin modes at the interface of topological nontrivial lattices and trivial lattices of the same frequency, which is consistent with Fig.11 is corresponding to Fig.11 Each characteristic frequency in the topological band gap corresponds to two degenerate states, and the pseudospin directions of the two degenerate states are different. The energy with a certain pseudospin direction can only propagate along a fixed direction, which is consistent with the characteristics of the quantum Hall effect.

[0063] Since the proposed structure is able to support topological boundary states, this unique property can be exploited to realize new functional devices. Fig.13 As shown in the figure, the structure is composed of topological non-trivial primitive cells and topological mediocre primitive cells. The top and bottom of the blue and red dashed lines are topological non-trivial lattices and topological mediocre lattices respectively. The interface between the non-trivial primitive cells and the mediocre primitive cells is a bending curve. The blue and red dashed lines are two different types of splicing interfaces. The blue dashed line is a zigzag interface, where the primitive cell structure is intact; the red dashed line is a broken armchair interface, where the primitive cell structure is divided into two halves. Directional waveguide structures can be constructed by splicing two different types of lattices.

[0064] Place a point sound source at the left port at the interface between the non-trivial unit cell and the trivial unit cell (at Fig.14 Indicated by a yellow five-pointed star), Fig.14 This is the sound pressure field diagram of the bent acoustic waveguide structure under the excitation source frequency of 1115.9Hz. It can be found from the sound pressure field diagram that due to the existence of topologically protected boundary states at the interface between non-trivial and ordinary splicing, even if the interface is in a curved shape, the sound wave can propagate forward along the interface, and the backscattering is suppressed, so high-transmittance backscattering-free sound transmission can be achieved. Therefore, the topologically protected interface states can be used to construct acoustic waveguide devices.

[0065] In order to further verify the robustness of sound wave propagation along the sharp bend interface, Fig.15 As shown in Figure 1, defects are introduced by removing the air cavities at the interface between the topological non-trivial lattice and the topological trivial lattice (two air cavities on the front and back sides of the topological non-trivial lattice and six air cavities on the front and back sides of the topological trivial lattice are removed). Similarly, a point sound source is placed at the left port at the interface between the non-trivial unit cell and the trivial unit cell to excite at the same frequency. The sound pressure field of the structure after the defect is introduced is as follows: Fig.16 As shown in the figure, the pseudospin-related boundary modes can bypass the defects in the topological waveguide, and the sound waves still propagate stably along the bent interface, which is basically the same as the sound propagation characteristics corresponding to the defect-free acoustic topological waveguide. This shows that the edge mode is almost unaffected by the defect-induced backscattering. Therefore, this non-trivial edge state transmission is robust.

[0066] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A two-dimensional hexagonal lattice phononic crystal, characterized in that: The invention comprises an air plate (1) and a resonant cavity (2), wherein the resonant cavity (2) is arranged in a plurality and all are arranged on the air plate (1), and the bottom is connected to the air plate (1) to form a composite primitive cell, and energy band inversion is achieved by changing the distance between the resonant cavities (2) on one side of the air plate (1), thereby realizing the acoustic quantum spin Hall effect; and further comprises: a topologically non-trivial primitive cell and a topologically trivial primitive cell; the distance between the resonant cavities (2) on the lower surface of the air plate (1) of the topologically non-trivial primitive cell and the topologically trivial primitive cell is the same, and the distance between the resonant cavities (2) on the upper surface of the air plate (1) is different.

2. A two-dimensional hexagonal lattice phononic crystal according to claim 1, characterized in that: The number of the resonant cavities (2) is set to an even number, and a plurality of the resonant cavities (2) are divided into two groups and are arranged on two surfaces of the air plate (1).

3. A two-dimensional hexagonal lattice phononic crystal according to claim 2, characterized in that: The number of the resonant cavities (2) is set to 12, and the 12 resonant cavities (2) are divided into two groups and are arranged on two surfaces of the air plate (1).

4. A two-dimensional hexagonal lattice phononic crystal according to claim 3, characterized in that: Any one of the resonant cavities (2) is a hollow cylinder, and the bottom of the hollow cylinder is connected to the air plate (1).

5. A two-dimensional hexagonal lattice phononic crystal according to claim 4, characterized in that: The surface of the air plate (1) is a hexagon, and the centers of the six resonant cavities (2) on each surface are located on the perpendicular midline of each side of the hexagon.

6. A waveguide structure, characterized in that: The invention comprises a two-dimensional hexagonal lattice phononic crystal as described in several claims 1.

7. A waveguide structure according to claim 6, characterized in that: A finite hexagonal acoustic structure is formed by splicing several topological non-trivial primitive cells and several topological trivial primitive cells.

8. A waveguide structure according to claim 7, characterized in that: The left and right sides of the finite hexagonal acoustic structure are each composed of a number of topologically trivial primitive cells, and the middle part is composed of topologically non-trivial primitive cells.

9. A waveguide structure according to claim 8, characterized in that: The interface between the topological non-trivial primitive cell and the topological trivial primitive cell is a curved curve, and the interface includes a zigzag interface and a broken armchair interface.

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