Multiband valley topological insulator based on clover-like scatterers

Abstract

The present invention discloses a multi-band valley topological insulator based on a clover-shaped scatterer, wherein the valley topological insulator comprises a unit cell, wherein the unit cell consists of a regular hexagonal carrier and a structure having a clover-shaped scatterer, and the center of the clover-shaped scatterer coincides with the center of the regular hexagonal carrier. The structure of the present invention is simple to process and prepare, and has a wide range of applications, and is expected to provide ideas and methods for designing multi-band and multi-functional acoustic topological devices with a relatively simple single structure.

Description

Technical Field

[0001] The present invention relates to topological boundary states of acoustic metamaterials, accidental degenerate double points of acoustic topological insulators, valley topological effects, and acoustic propagation regulation, and in particular to a multi-band valley topological insulator based on a clover-shaped scatterer. Background Art

[0002] One of the most interesting advances in condensed matter physics is the discovery of a new state of matter called topologically ordered states. Topology simply means different shapes and topological equivalence. Topological states were all first observed in electronic materials and were initially thought to be closely related to the Fermi-Dirac statistics of electrons. Because the speed of sound is several orders of magnitude lower than the speed of light, phonon information processing has unique advantages in terms of smaller wavelengths and stronger phonon-phonon interactions than photonic systems. The resulting slow group velocity and high density of states enhance backscattering, making phononic systems more susceptible to disorder than photonic systems. The huge contrast in acoustic impedance between ordinary materials further promotes disordered backscattering. Phononic crystals have become an ideal platform for realizing and testing topological acoustics due to their controllable defects and structures, and convenient preparation and observation. The discovery of topological acoustics not only allows people to re-understand the phenomenon of sound transmission, but also expands the design methods of acoustic wave control devices, and arouses people's interest in the study of topology in the field of acoustic waves.

[0003] In addition to the intrinsic spin freedom, electrons in crystals also have valley freedom, where valleys are extreme points in the band structure. Liu Zhengyou, Qiu Chunyin and others introduced the concept of valley states in electronic systems into two-dimensional phononic crystals, and realized acoustic topological valley state transport at the interface composed of two phononic crystals with different acoustic valley Hall phases. Zhang Baile and others realized similar edge states in topological waveguides composed of hexagonal lattice phononic crystals, which can also support acoustic topological valley state transport. Lu Jiuyang and others observed valley topological phases in double-layer phononic crystals by using interlayer coupling and changes in the rotation angle of regular triangle scatterers in a double-layer phononic crystal structure. Valley-based topological edge states have attracted widespread attention due to their backscattering suppression and immune deficiency characteristics of acoustic transmission, and have been widely used to design various acoustic wave-based devices, such as acoustic delay lines and robust programmable waveguides. However, most existing acoustic topological insulators are limited to a single operating frequency band, and there are still great challenges in designing multi-band acoustic devices.

[0004] Based on this, the present invention designs a honeycomb topology structure unit based on a clover-shaped scatterer. By adjusting the structural parameters of the honeycomb structure unit, the phononic crystal has multiple linear Dirac degenerate points at the K point in the Brillouin zone at the same time. By rotating the clover-shaped scatterer, the mirror symmetry of the structure is broken, thereby opening the degeneracy at the Dirac point, and multi-channel acoustic communication can be achieved. This provides ideas and methods for designing multi-band and multi-functional acoustic topology devices using a single structure. Summary of the invention

[0005] The object of the present invention is to provide a multi-band valley topological insulator based on a clover-shaped scatterer.

[0006] In order to achieve the above-mentioned invention object, the present invention adopts the following technical solutions:

[0007] A multi-band valley topological insulator based on a clover-shaped scatterer, wherein the valley topological insulator comprises a unit cell, wherein the unit cell consists of a regular hexagonal carrier and a structure having a clover-shaped scatterer; and the center of the clover-shaped scatterer coincides with the center of the regular hexagonal carrier.

[0008] The lattice constant of the unit cell is a, the radius of the clover-shaped scatterer is R, and the rotation angle is θ, where R<0.5a.

[0009] The multi-band valley topological insulator based on the clover-shaped scatterer, the clover-shaped scatterer is a rigid body, and the air density between the clover-shaped scatterers is p=1.21Kg / m 3 , the speed of sound c = 343m / s. Rigid body means that the clover-shaped scatterer is made of hard materials, such as metal, alloy, etc.

[0010] The lattice constant of the unit cell is a=10mm. By adjusting the structural parameters of the cloverleaf scatterer, the deterministic degenerate points are obtained at the K-point frequencies of 18.6KHz, 38.8KHz, and 53.3KHz. At this time, the structural parameters corresponding to the cloverleaf scatterer are R=3.5 and θ=0°. By rotating the cloverleaf scatterer, the mirror symmetry of the structure is broken, thereby opening the degeneracy at the Dirac point and obtaining a structure with acoustic pseudospin and topological boundary states.

[0011] Compared with the prior art, the present invention has the following technical effects:

[0012] The present invention discloses a single-structure multi-band multifunctional valley topological insulator with abundant adjustable parameters (R, θ). 3v Symmetry, which causes deterministic degeneracy caused by band gap closure at high symmetry points in the first Brillouin zone. Rotating the cloverleaf scatterers in the phononic crystal will break the structural symmetry, thereby realizing the valley Hall phase transition. By adjusting the structural parameters of the honeycomb structure unit, the phononic crystal has multiple linear Dirac degenerate points at the K point in the Brillouin zone, which can realize multi-channel acoustic communication. Rotating the cloverleaf scatterer changes θ to break the mirror symmetry of the lattice system, thereby realizing the valley Hall phase transition. When θ = -20°, K + State in K - Upper part, m>0; when θ=20°, K - State in K+ Upper part, m<0. The vortex chirality shows that when the rotation angle is reversed, the vortex chirality of the corresponding valley is reversed, and valley topological acoustic transport can be realized. The valley pseudospin state can be flexibly adjusted by simply rotating the clover-shaped scatterer without rebuilding the phononic crystal. When the clover-shaped scatterer rotates clockwise from -60° to 60°, the band gap undergoes an open-close-open process, an energy band inversion occurs, and a topological phase transition is realized. The present invention explores a new method for the design of acoustic wave regulation, laying a foundation for the engineering application of multi-functional acoustic devices such as multi-band acoustic antennas and acoustic logic control.

[0013] The present invention designs the acoustic topological insulator based on the quantum spin Hall effect of the clover-shaped scatterer. By using the body state-boundary state correspondence principle and connecting different structural systems, the boundary state is constructed to simulate the topologically protected edge acoustic transmission. Different phononic crystal structures are further constructed, and the topological boundary state's acoustic transmission characteristics are verified by the finite element algorithm. The structure of the present invention is simple to process and prepare, and has a wide range of applications. It is expected to provide ideas and methods for designing multi-band and multi-functional acoustic topological devices with a relatively simple single structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 (a) Honeycomb topological structural unit of the cloverleaf scatterer; (b) Structural diagram of the cloverleaf scatterer; (c) Simple arrangement and combination diagram of the topological structural unit.

[0015] Figure 2 (a) The frequency curve of the double Dirac cone of the structural unit at the Γ point varies with θ; (b) The corresponding band structure when θ = 0°; (c) The corresponding band structure when θ = -20°; (d) The corresponding band structure when θ = 20°.

[0016] Figure 3 (a)-(c) Absolute sound pressure field and phase of K1-K3 and direction of energy flow. The rainbow colors represent the absolute sound pressure field and phase, and the arrows represent the magnitude and direction of energy flow.

[0017] Figure 4 (a), (c), and (e) represent the modal distribution of the K1-K3 valley state supercell, where energy propagates only at the boundary states; (b), (d), and (f) represent the band diagrams of the K1-K3 valley state supercell structure, where the red and blue lines represent the boundary states and the black area represents the bulk state.

[0018] Figure 5 (a)-(c) Transmission of the K1-K3 valley state in structure I where the topological and non-topological structures constitute a straight boundary; (d)-(f) Transmission of the K1-K3 valley state in structure II where the topological and non-topological structures constitute a broken line boundary with four right-angle turns.

[0019] Figure 6 (a) The trend of the band structure at point K changing with the radius R; (b) The band structure at point K when R = 3.6 mm.

[0020] Figure 7 (a) Honeycomb topological structural unit of a triangular scatterer; (b) The frequency curve of the double Dirac cone of the structural unit at the Γ point as a inverse function of θ1; (c) The K4 valley energy band structure corresponding to the honeycomb topological structural unit of a triangular scatterer when θ = 20°; (d) The K1 valley energy band structure corresponding to the honeycomb topological structural unit of a cloverleaf scatterer when θ = 20°. DETAILED DESCRIPTION

[0021] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. The technical solution of the present invention is described in detail below. The embodiments described with reference to the accompanying drawings are exemplary and cannot be understood as limiting the present invention. All other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] Example 1

[0023] The multi-band valley topological insulator based on the clover-shaped scatterer proposed in the present invention comprises a unit cell, wherein the unit cell consists of a regular hexagonal carrier and a structure with a clover-shaped scatterer, such as Figure 1 (a) shows that the lattice constant is a, the gray area is air, and the white area is a rigid body. The unit cell unit forms a honeycomb topological structure unit with a clover-shaped scatterer, such as Figure 1 (c) Figure 1 (c) is just a schematic diagram of the simple arrangement and combination of topological structural units. In order to illustrate the structure of the valley topological insulator, the insulator is divided into several regular hexagonal carriers, on which a clover scatterer structure is fixed. When designing its structure, the clover-shaped scatterer is obtained by rotating a circle with a radius of R upward and downward by 120°, and then performing a Boolean operation. The center of the clover-shaped scatterer coincides with the center of the regular hexagonal carrier, and the rotation angle of the clover-shaped scatterer is θ. Studies have shown that because the designed structural system has C 3v Symmetry, the honeycomb topological structural unit with clover-shaped scatterers will cause deterministic degeneracy caused by band gap closure at high symmetry points in the first Brillouin zone. The clover-shaped scatterers in the rotating phononic crystal will break the structural mirror symmetry, thus realizing the valley Hall phase transition.

[0024] In order to study the energy band structure and transmission characteristics of the designed structure, the present invention uses the finite element analysis software COMSOL Multiphysics to perform numerical calculations to study the energy band structure and transmission characteristics of the phononic crystal, fixing the lattice constant a = 10 mm and the air density p = 1.21 kg / m 3 , the speed of sound c = 343 m / s. The four outer boundaries of the structural unit are set as periodic boundary conditions for band structure calculation. The band structure is calculated by solving the characteristic frequency equation and scanning the wave k in the first Brillouin zone of the honeycomb lattice in the reciprocal lattice space.

[0025] By adjusting the structural parameters, when θ = 0°, the honeycomb topological structural unit has mirror symmetry on the y-axis, and a deterministic degenerate point is obtained at the K point in the first Brillouin zone, such as Figure 2 (b) is shown. At this time, the corresponding structural parameter is R = 3.5. Since the dispersion relation near the Dirac point is approximately linear, it is easy to break the symmetry of the lattice system by adjusting the material properties and geometric parameters. The present invention breaks the mirror symmetry of the lattice system by changing θ, thereby achieving the valley Hall phase transition. When the other structural parameters of the honeycomb structure unit remain unchanged, the curve of the frequency at the high symmetry point K changing with θ is shown in Figure 2 As shown in (a), the definite degenerate points are obtained at the K-point frequencies of 18.6KHz, 38.8KHz, and 53.3KHz. When the clover-shaped scatterer rotates, due to the incomplete symmetry, the irreducible representation of the degenerate E is transformed into two non-degenerate irreducible representations E1 and E2. The three degenerate states at the K-point are split to form the body energy band gap, and the three Dirac cones are opened to form three pairs of valley states, marked as K1, K2, and K3. The band structure of the phononic crystal composed of the rotating clover-shaped scatterer θ = -20° is shown in Figure 2 (b) As shown; the band structure of the phononic crystal composed of a clover-shaped scatterer rotated by θ = 20° is shown in Figure 2 (d) as shown.

[0026] The absolute pressure field, intensity and phase distribution near the band gap corresponding to the three pairs of valley states K1, K2 and K3 are shown in Figure 3 These valley pseudospin states have rotational chirality similar to that of electronic spin states, and the acoustic valley pseudospin states exhibit different vortex chirality and phase. When the vortex chirality of the corresponding valley state is right-handed, it is marked as K + ; When the vortex chirality corresponding to the valley state is left-handed, it is marked as K - . Effective mass In the formula and is the frequency corresponding to the valley eigenstate, v D is the Dirac velocity. When θ=-20°, K + State in K -Upper part, m>0; when θ=20°, K - State in K + In the upper part, m<0. The chirality of the vortex indicates that when the rotation angle is reversed, the chirality of the vortex of the corresponding valley is reversed, and the effective mass m near the corresponding Dirac cone has the opposite sign. Therefore, the valley Chern number C of the two types of phononic crystals is K = ±1 / 2sgn(M) On the contrary, with different acoustic valley Hall phases, valley topological acoustic transport can be realized. Valley pseudospin states can be flexibly adjusted by simply rotating the clover-shaped scatterer without reconstructing the phononic crystal. When the clover-shaped scatterer rotates clockwise from -60° to 60°, the band gap undergoes an open-close-open process, and an energy band inversion occurs, realizing a topological phase transition.

[0027] In order to verify the characteristics of topologically protected boundary states, topologically trivial structures and non-trivial structures are combined to construct a supercell. The supercell is arranged linearly along the x direction and consists of 12 structures with θ=-20° and 12 structures with θ=20°. Figure 4 (a), (c), and (e) reflect the characteristics of topological boundary state transmission. The sound waves only propagate locally at the boundary and do not spread to both sides. Figure 4 (b), (d), and (f) are the dispersion relations of the supercell of the valley topological acoustic waveguide near the Dirac point. There are topological boundary states that cross the entire band gap on the boundary represented by the red and blue lines in the band gap, while the black area represents the bulk state. The modal distribution of the boundary state shows that the sound wave is mainly confined to the domain wall, which is consistent with the band structure. Each interface contains a pair of edge states with the same sound speed but opposite propagation directions. The generation of this topological boundary state originates from the fact that the structures at both ends of the boundary have different topological valley Chern numbers. When the structures on both sides of the boundary have different-signed effective masses m, there will be topological boundary states without backscattering on the boundary. Figure 4 The left side of the supercell in θ is composed of structures with θ = -20° (m>0), while the right side is composed of structures with θ = 20° (m<0), so the change of the valley number across the boundary is This indicates that the edge state of K valley excitation will propagate in the reverse direction along the negative boundary. Similarly, the topological edge state of K′ valley excitation propagates in the positive direction due to ΔC(K′)=1. Therefore, the intersection position at the same frequency at the boundary corresponds to two different valley pseudospin states, which can realize pseudospin-related acoustic transmission.

[0028] An important property of topological boundary states is the robustness of their boundary transmission. Regardless of whether it is a straight or curved boundary, the topologically protected boundary states can achieve transmission with almost no reflection and loss. Figure 5 As shown in (a)-(c), the structure I with a straight line boundary is composed of two units of θ°=20° and θ°=-20°. When excitation is applied on the left side, it can be found that the sound wave is transmitted along the straight line boundary without hindrance. Figure 5 As shown in (d)-(f), the structure II with four right-angle turns is composed of two units of θ°=20° and θ°=-20°. When the excitation is applied on the left side, the sound wave is also transmitted along the boundary state without hindrance, just like the straight line transmission. This is because there is a topologically protected boundary state at the junction of non-trivial and mediocre structures. Even if the interface is irregularly shaped such as bending, the sound wave can propagate along the interface. At the same time, when the sound wave propagates from the boundary to both sides, the energy will decay rapidly, so that the sound wave can only propagate forward along the interface. Figure 5 The structures shown in (c) and (f) are not very ideal for acoustic wave localization during acoustic transmission, and there is a slight scattering effect on both sides of the boundary state. This is mainly due to the high frequency of the K3 valley state and the narrow band gap. The present invention explores a new method for acoustic wave control design, laying a foundation for the engineering application of multi-functional acoustic devices such as multi-band acoustic antennas and acoustic logic control.

[0029] Comparative Example 1

[0030] like Figure 6 As shown in (a), the trend of the band structure at point K changing with radius R shows that as R increases, the band gaps of the two valley states K1 and K2 gradually expand. Figure 6 (b) shows the band structure of point K when R = 3.6 mm. The valley state of K3 forms a closure with the previous band at the closure point, which affects its transmission characteristics and robustness. After comprehensive consideration, the present invention adopts R = 3.5 mm as an embodiment.

[0031] Comparative Example 2

[0032] The honeycomb topology unit using triangular scatterers instead of clover-shaped scatterers is as follows Figure 7 (a) shows that the equilateral triangle is inscribed in a circle with a radius of R = 3.5 mm. The rotation angle is θ1. Compared with the comparative experiment, the embodiment of the present invention has the following advantages: 1) Figure 2 (a) and Figure 7 As shown in (b), under the condition of the same circle radius R and rotation angle, the embodiment has three valley states K1-K3, while the comparative example only has two valley states K4 and K5. The application range of the embodiment is wider than that of the comparative experiment; 2) Figure 7 (c) and Figure 7 As shown in (d), it can be seen that when θ = 20°, the band gap of the K4 valley energy band structure corresponding to the comparative experiment is 3069 Hz, while when θ = 20°, the band gap of the K1 valley energy band structure corresponding to the embodiment is 3312 Hz. The band gap of the embodiment is wider and has better robustness. Therefore, the present invention adopts a honeycomb topological structure unit of a clover-shaped scatterer.

[0033] Finally, it should be noted that the above is only a specific embodiment of the present invention. Obviously, the present invention is not limited to the above embodiment, and all variations that can be directly derived or associated with the content disclosed by ordinary technicians in this field should be considered as the protection scope of the present invention.

Claims

1. A multi-band valley topological insulator based on a clover-shaped scatterer, characterized in that The valley topological insulator comprises a unit cell, which is composed of a regular hexagonal carrier and a structure with a clover-shaped scatterer, and the center of the clover-shaped scatterer coincides with the center of the regular hexagonal carrier.

2. The multi-band valley topological insulator based on a clover-shaped scatterer according to claim 1, characterized in that: The lattice constant of the unit cell is a, the radius of the clover-shaped scatterer is R, and the rotation angle is θ, where R<0.5a.

3. The multi-band valley topological insulator based on a clover-shaped scatterer according to claim 1, characterized in that: The clover-shaped scatterer is a rigid body, and the air density between the clover-shaped scatterers is p=1.21Kg / m 3 , speed of sound c = 343m / s.

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