A temperature-tunable acoustic topological insulator

Abstract

The application provides a temperature-adjustable acoustic topological insulator. By adjusting the environmental temperature, the four-fold Dirac point degeneracy at the Gamma point can be opened, resulting in the band inversion between the two-fold degenerate dipole state and quadrupole state, and a topological phase transition is realized. The evolution law of the topological state with temperature is numerically studied, and a new type of topological acoustic switch is constructed. By controlling the topological phase through temperature, the non-contact active regulation of the interface state in the structure can be realized, and the switching effect is exhibited. The research of the application can provide a corresponding reference for the intelligent control of sound and vibration of acoustic topology.

Description

Technical Field

[0001] This invention belongs to the field of acoustic metamaterials, specifically relating to a temperature-tunable acoustic topological insulator. Background Technology

[0002] The emergence of acoustic artificial materials (including phononic crystals and acoustic metamaterials) has provided new means for the manipulation of sound waves and elastic waves. Acoustic artificial materials are artificially designed composite structures; by designing different structural units, many unique physical properties not found in natural materials can be obtained, such as band gaps, negative equivalent mass, and negative equivalent modulus. As research into acoustic artificial materials deepens, researchers are attempting to integrate them with other disciplines. In recent years, the introduction of topological phases from condensed matter physics into acoustic artificial materials has attracted considerable attention.

[0003] However, traditional acoustic topological insulators lack adjustable bandgap properties after structural design, thus failing to meet the requirements of different working environments and limiting their application range. Furthermore, existing research has found that the thermal environment has a certain impact on the propagation and topological properties of elastic waves, but this research mainly focuses on the influence of the thermal environment on the material's physical properties. There are few studies considering the influence of thermal stress on the band structure of acoustic topological insulators, and no research has yet been found that simultaneously considers the control of topological properties by thermal stress and material physical properties. Summary of the Invention

[0004] The purpose of this invention is to study the evolution of band structure characteristics of a two-dimensional binary honeycomb phononic crystal constructed from tungsten-epoxy resin, taking thermal stress as the research object. By controlling the ambient temperature to open the quadruple Dirac point degeneracy at the Γ point, a topological phase transition of the phononic crystal is achieved, thus constructing a temperature-controllable acoustic switch. The frequency range and topological interface of its topological state are controlled by the ambient temperature, realizing non-contact active control of the topological state.

[0005] The technical solution of the present invention is as follows:

[0006] The present invention provides a temperature-adjustable acoustic topological insulator composed of a plurality of regular hexagonal honeycomb lattices, each regular hexagonal honeycomb lattice including six additional counterweights.

[0007] Furthermore, the side length a of the regular hexagonal honeycomb lattice is 12 mm.

[0008] Furthermore, the six additional weights are located at the six vertices of the regular hexagonal honeycomb lattice.

[0009] Furthermore, the additional counterweight is an equilateral triangle with side length w, where side length w = 4.6 mm.

[0010] Furthermore, the regular hexagonal honeycomb lattice is composed of tungsten and polyurethane, wherein the density r of the polyurethane is... Exp =1180kg / m 3 Young's modulus E of polyurethane Exp =0.559 GPa, Poisson's ratio c of polyurethane Exp =0.368; the density r of the tungsten metal Exp =19100kg / m 3 Poisson's ratio c of metallic tungsten Exp =0.35.

[0011] Furthermore, the Young's modulus of the tungsten metal is temperature-dependent.

[0012] Furthermore, by adjusting the ambient temperature, the energy bands formed by several regular hexagonal honeycomb lattices can be flipped to achieve a topological phase transition, and the position and width of the band gap can be controlled.

[0013] Furthermore, the interface state formed between tungsten and polyurethane can be adjusted by changing the temperature.

[0014] Technical effects of the present invention:

[0015] This invention studies a tunable acoustic metamaterial composed of a two-dimensional binary honeycomb structure. By adjusting the ambient temperature, the quadruple Dirac point degeneracy at the Γ point can be opened, causing a band reversal and thus achieving a topological phase transition. Based on the volume-boundary correspondence principle, a two-dimensional supercell is constructed using two types of unit cell structures for topological phase transition. Without changing the structure, the dispersion relation of the supercell can be dynamically adjusted by changing the temperature, allowing for effective control over the location of interface states. Furthermore, the presence of interface states can be adjusted from none to all, exhibiting an acoustic switching effect. This invention provides a reliable reference for the practical application of interface states in tunable filters and multi-channel filters. Attached Figure Description

[0016] The accompanying drawings illustrate various embodiments generally by way of example rather than limitation, and are used, together with the specification and claims, to explain embodiments of the invention. Where appropriate, the same reference numerals are used in all drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the apparatus or method.

[0017] Figure 1 A schematic diagram of the acoustic metamaterial I of the present invention and a corresponding energy band diagram are shown.

[0018] Figure 2 The diagram shows the structural band structure of the acoustic metamaterial I of the present invention at different temperatures;

[0019] Figure 3 This diagram illustrates the displacement field distribution corresponding to the degenerate eigenstate at point Γ in this invention.

[0020] Figure 4 A schematic diagram showing the variation curve of the bandgap boundary frequency of the present invention with temperature is shown.

[0021] Figure 5 A schematic diagram showing the evolution of the band structure of the acoustic metamaterial structure II (t = 0.04 mm) of the present invention at different temperatures is shown.

[0022] Figure 6 The diagram shows a schematic of the 6(a) supercell structure of the present invention, and a schematic diagram of the change of intrinsic frequencies with temperature.

[0023] Figure 7 The topological supercell projection band diagrams of the present invention at ΔT = 70℃ and ΔT = -70℃ are shown.

[0024] Figure 8 The transmission of the acoustic switch at ΔT = -70°C and ΔT = 70°C according to the present invention is shown. Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] The two-dimensional binary honeycomb structure unit proposed in this embodiment of the invention is shown in Figure 1(a). This structure is a regular hexagonal honeycomb lattice (side length a = 12 mm, side width t) composed of six metal arms. Six additional counterweights (equilateral triangular regions with side length w enclosed by dashed lines in the figure) are located at the vertices of the hexagon, where w = 4.6 mm and the lattice constant is... The gray area in the figure represents polyurethane (density r). Exp =1180kg / m 3 Young's modulus E Exp =0.559 GPa, Poisson's ratio c Exp =0.368), the light gray part is metallic tungsten (density r Exp =19100kg / m 3 Poisson's ratio c Exp =0.35). The Young's modulus of metallic tungsten is temperature-dependent (T) E = 391.448 - 1.3160 ​​× 10⁻⁶. -2 ×T-1.4838×10 -5 ×T 2 .

[0027] This invention employs the solid mechanics module of COMSOL Multiphysics to calculate the band structure and displacement field distribution of elastic waves in the phononic crystal. When solving the bulk (edge) band dispersion relation, Floquet periodic boundary conditions are applied to the periodic surfaces of the unit cell (supercell). Figure 1 (b) shows the band structure of acoustic metamaterial I at room temperature (20℃, i.e., ΔT = 0℃), where the hexagonal side width t = 0.164 mm. It can be clearly seen that its band gap closes at 43.85 kHz, forming a fourfold accidental degenerate Dirac point. At this point, it exhibits a double Dirac cone characteristic at the center of the Brillouin zone.

[0028] The effect of temperature on acoustic bands

[0029] Previous studies have shown that the topological bandgap of acoustic topological metamaterials with fixed structures is not tunable. Furthermore, ambient temperature has a significant impact on the inherent vibrational characteristics and dynamic response of the structure. Therefore, this study investigated the evolution of the bandgap properties of acoustic topological metamaterials under different ambient temperatures. Figure 2 The band structure diagrams of this acoustic metamaterial at different temperatures ΔT = -70℃ and ΔT = 70℃ are presented. As can be seen from the diagrams, the temperature change causes the fourfold degenerate state at the Dirac point to split into two double degenerate states, forming a topologically complete bandgap. The degenerate eigenstates at the Γ point are marked by blue and red dots. The displacement field distributions corresponding to these double degenerate states are shown below. Figure 3 As shown, for ΔT = -70℃, the doubly degenerate state above the band gap is a pseudospin quadrupole mode (d state), and the state below the band gap is a pseudospin dipole mode (p state), exhibiting a topologically trivial phase. However, at ΔT = 70℃, the band gap still exists, but the band positions of the p and d states are reversed; that is, the doubly degenerate state above the band gap is a d state, and the state below the band gap is a p state, exhibiting a topologically nontrivial phase. This means that temperature changes can cause band reversal and induce a topological phase transition.

[0030] To further reveal the influence of temperature on the topological properties of acoustic metamaterials, the bandgap boundary frequency as a function of temperature is shown in the following figure. Figure 4 As shown, the blue and red lines correspond to the quadrupole mode (d-state) and dipole mode (p-state), respectively. It can be observed that as the temperature changes from ΔT = -120℃ to ΔT = 120℃, the energy bands are all shifted to lower frequencies, and the band gap undergoes a process of opening, closing, and then opening again. When ΔT < 0, the band gap is topologically trivial; when ΔT > 0, the band gap is topologically non-trivial. The topological properties of the energy bands change before and after ΔT = 0℃. Therefore, by controlling the ambient temperature, a topological phase transition can be achieved by inverting the energy bands, and the position and width of the band gap can be controlled, realizing non-contact active control of the topological states.

[0031] Temperature regulation of interface states

[0032] Since interface states only exist when two materials with different topological properties share a common band gap, the band structure evolution of the acoustic metamaterial structure II (t = 0.04 mm) at different temperatures was calculated. Figure 5 It can be seen that the band structure exhibits only topologically trivial bands and shares a common bandgap with acoustic metamaterial structure I. According to the bulk-boundary correspondence principle, interface states must exist at the interface between the topologically nontrivial phononic crystal and the topologically trivial phononic crystal. For example... Figure 6 As shown in (a), a supercell composed of acoustic metamaterials I and II was constructed. Figure 6 (b) shows the frequency variation of the entire supercell with temperature. It can be seen that when ΔT>0, the interface states exist in the common bandgap of the system, and when ΔT<0, the interface states disappear. Further analysis shows that when ΔT>0, the bandgap of acoustic metamaterial I in the supercell is topologically nontrivial, while the bandgap of acoustic metamaterial II is topologically trivial; therefore, interface states exist in the supercell. When ΔT<0, the bandgap on both sides of the supercell is topologically trivial; therefore, the interface states will disappear. Figure 7 This is a projection band structure diagram of the supercell along the Γ-K direction at ΔT = 70℃ and ΔT = -70℃. It can be seen that... Figure 6 In (a), a pair of edge states with band gaps appear within the volume bandgap in the frequency range of 40.9 kHz–41.9 kHz, marked by the red and blue curves respectively. Meanwhile... Figure 6 (b) contains only the bulk bandgap. Therefore, without changing the structure, the interface states can be made to disappear or appear simply by changing the temperature, thus achieving the regulation of the interface states.

[0033] To further study its temperature control effect, a topological acoustic straight waveguide composed of acoustic metamaterials I and II was constructed. Figure 7 The intrinsic displacement field of out-of-plane vibration at ΔT = 70℃ is given. It can be seen that the edge states are well localized near the two-phase interface. Since there is no bulk propagation mode within the bandgap, the edge states decay rapidly on both sides perpendicular to the interface. Figure 8 The intrinsic displacement field of out-of-plane vibration at ΔT = -70℃ is given, showing that sound waves cannot propagate. Thus, the effect of a sound switch is achieved by changing the temperature.

[0034] in conclusion

[0035] This invention studies a tunable acoustic metamaterial composed of a two-dimensional binary honeycomb structure. By adjusting the ambient temperature, the quadruple Dirac point degeneracy at the Γ point can be opened, causing a band reversal and thus realizing a topological phase transition. Based on the volume-boundary correspondence principle, a two-dimensional supercell was constructed using two types of unit cell structures for topological phase transition. Without changing the structure, the dispersion relation of the supercell can be dynamically adjusted by changing the temperature, allowing for effective control over the location of interface states. Furthermore, the presence of interface states can be adjusted from none to all, exhibiting an acoustic switching effect. This research provides a reliable reference for the practical application of interface states in tunable filters and multi-channel filters.

[0036] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the technical scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A temperature-adjustable acoustic topological insulator, characterized in that, It consists of several regular hexagonal honeycomb lattices, each of which includes six additional weights; The regular hexagonal honeycomb lattice is composed of metallic tungsten and polyurethane, wherein the density of the polyurethane is... Young's modulus of polyurethane Poisson's ratio of polyurethane The density of the tungsten metal Poisson's ratio of metallic tungsten ; By adjusting the ambient temperature, the energy bands formed by several regular hexagonal honeycomb lattices can be flipped to achieve a topological phase transition, and the position and width of the band gap can be controlled. The interface state between tungsten and polyurethane can be adjusted by changing the temperature. The topological phase transition is specifically achieved by adjusting the ambient temperature to break the quadruple Dirac point degeneracy at the Γ point, thereby causing the energy band to flip. The adjustment of the interface state is based on the volume-boundary correspondence principle. A two-dimensional supercell is constructed using two types of primitive cell structures of the topological phase transition, so as to adjust the interface state from nothing to something without changing the structure.

2. The temperature-adjustable acoustic topological insulator according to claim 1, characterized in that, The side length a of the regular hexagonal honeycomb lattice is 12 mm.

3. The temperature-adjustable acoustic topological insulator according to claim 1, characterized in that, The six additional weights are located at the six vertices of the regular hexagonal honeycomb lattice.

4. The temperature-adjustable acoustic topological insulator according to claim 1, characterized in that, The additional counterweight is an equilateral triangle with side length w, where w = 4.6 mm.

5. The temperature-adjustable acoustic topological insulator according to claim 1, characterized in that, The Young's modulus of the tungsten metal is temperature-dependent.

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