CN114710132A

CN114710132A - Elastic wave topological insulator with electrically adjustable frequency and functional component

Info

Publication number: CN114710132A
Application number: CN202110580747.9A
Authority: CN
Inventors: 余思远; 张子栋; 成程; 卢明辉; 陈延峰
Original assignee: Nanjing University
Current assignee: Nanjing University
Priority date: 2021-05-26
Filing date: 2021-05-26
Publication date: 2022-07-05
Anticipated expiration: 2041-05-26
Also published as: CN114710132B

Abstract

The invention provides an elastic wave topological insulator with electrically adjustable frequency and a functional component, wherein the elastic wave topological insulator comprises a substrate and a two-dimensional material layer, the two-dimensional material layer is tiled on the substrate, a honeycomb lattice pattern is arranged on the surface of the substrate, the two-dimensional material layer comprises a first area and a suspended second area, the first area is in contact with the substrate, acoustic impedance of the second area is mismatched with that of the substrate, and the two-dimensional material layer is constructed into a phononic crystal structure. The invention can realize the frequency electric adjustability of the elastic wave topological insulator.

Description

Elastic wave topological insulator with electrically adjustable frequency and functional component

Technical Field

The invention relates to the field of atomic thin films, in particular to an elastic topological insulator with electrically adjustable frequency and a functional assembly.

Background

In practical device applications, accurate control of elastic waves in the spatial and frequency domains is always sought. Compared to acoustic waves in fluids (e.g., airborne sound), elastic waves have extremely low transmission losses at higher frequencies, making integration into solid state micro/nano-scale systems easier. Compared to electromagnetic waves, the area of a device using elastic waves is 5 orders of magnitude smaller than that of electromagnetic waves at the same operating frequency. These major advantages have led to the widespread use of Surface Acoustic Wave (SAWs) or Bulk Acoustic Wave (BAWs) devices in modern signal processing and sensors. Over the past decade, Topological Insulators (TI) have rapidly expanded from electronics to classical wave systems, leading to revolutionary transmission channels, mainly due to the "spin-momentum locking" characteristic of photons/phonons at their boundaries.

To date, elastic topological insulators have been implemented in both macroscopic and microscopic systems, such as perforated plates, le-gabby boards, and suspended nanofilms, which exhibit unprecedented functional components. The first-order elastic topological insulator provides a very ideal one-dimensional elastic waveguide technology, and (1) even if the waveguides rotate randomly or have internal defects, the transmitted energy cannot be lost. (2) Such a waveguide supports a broadband operating frequency without any dispersion. The second order elastic topological insulator provides a spatially zero-dimensional and frequency-dispersive state, which allows for purposeful localization of the elastic wave at specific frequencies and locations, such as at corners or intersections of topological boundaries. These ideal one-dimensional waveguides and 0-dimensional local area technologies enrich the means by which people control elastic waves to a large extent, and also generate some functional components, such as elastic topological resonators, filters, multiplexers, and the like. After the implementation of elastic topological insulators, a clear direction of research towards device applications is to miniaturize them and to achieve electrical tunability of frequencies, which is also a pressing need for advanced signal processors, sensors and the SAW and BAW industries. Recently, researchers have demonstrated some tunable, reconfigurable elastic topological insulators, such as Darabi et al, which have experimentally implemented reconfigurable electro-acoustic topological insulators by connecting programmable capacitive switches in a structured array of piezoelectric patches; zhou et al propose a method to achieve an adjustable elastic topological interface in a piezoelectric rod system with variable electrical boundaries. These components require complex external circuitry and are still limited to a macroscopic scale. Solutions for chip-level electrically tunable elastic TI are still lacking.

Disclosure of Invention

The invention aims to provide an elastic wave topological insulator and a functional component, so that the frequency of the elastic wave topological insulator can be electrically adjusted.

According to a first aspect of the present invention, an elastic wave topological insulator includes: the two-dimensional material layer is tiled on the substrate, a honeycomb lattice pattern is arranged on the surface of the substrate, the two-dimensional material layer comprises a first area in contact with the substrate and a suspended second area, the second area is mismatched with the acoustic impedance between the substrates, and the two-dimensional material layer is constructed into a phononic crystal structure.

Furthermore, the honeycomb lattice pattern is an array formed by hexagonal unit cells, each unit cell comprises six round holes which are sequentially crossed, and the distances between the centers of the six round holes in each unit cell and the centers of the unit cells in which the six round holes are located are equal.

Further, the honeycomb lattice pattern is a topologically mediocre lattice or a topologically non-mediocre lattice.

Further, the substrate is made of one of the following materials: SU-8 polymer, silicon dioxide, and piezoelectric GaAs.

Further, the two-dimensional material layer is made of graphene.

According to a second aspect of the invention, a functional assembly comprises said elastic wave topological insulator.

Further, the functional component is a beam splitter.

Further, the functional component is a resonator.

Further, the functional component is a filter.

Further, the functional component is a multiplexer.

The invention provides an elastic wave topological insulator and a functional component, a substrate and a two-dimensional material layer, wherein the two-dimensional material layer is tiled on the substrate, the surface of the substrate is provided with a honeycomb lattice pattern, the two-dimensional material layer comprises a first area in contact with the substrate and a suspended second area, the acoustic impedance between the second area and the substrate is mismatched, the two-dimensional material layer is constructed into a phonon crystal structure, and the two-dimensional material generally has electromechanical sensitivity, so that the mechanical property of the two-dimensional material layer can be easily adjusted by introducing grid voltage into the two-dimensional material layer.

Other characteristic features and advantages of the invention will become apparent from the following description of exemplary embodiments, which is to be read in connection with the accompanying drawings.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention. In the drawings, like reference numerals are used to indicate like elements. The drawings in the following description are directed to some, but not all embodiments of the invention. For a person skilled in the art, other figures can be derived from these figures without inventive effort.

Fig. 1a to fig. 1c are a schematic structural diagram, a top structural view and a side structural view of an embodiment of an elastic wave topological insulator of the present invention, respectively;

FIGS. 2 a-2 c are phononic crystal elastic wave dispersion curves of a substrate of an embodiment of an elastic wave topological insulator of the present invention;

FIG. 2d is a graph of the eigenfrequency of an embodiment of the elastic wave topological insulator of the present invention as a function of w above and below the band gap at the Γ point;

FIGS. 3a and 3b show band structures of elastic wave insulators corresponding to the centers of the circular holes at distances of 5.5 μm and 6.6 μm, respectively;

fig. 3c and 3d correspond to the intrinsic modes at the first three points of high symmetry of the energy bands of topologically mediocre and topologically non-mediocre lattices, respectively;

FIG. 4a is a schematic view of an elastic TI interface;

FIG. 4b is the calculated band structure for the TI boundary of FIG. 4 a;

FIGS. 4 c-4 e are schematic diagrams of an elastic function device made of TI boundaries;

FIGS. 5a and 5b are projected band diagrams of zigzag-type and broken armchair-type interfaces between an elastic wave topological insulator and a general insulator, respectively;

FIG. 5c is a top view and a bottom view of a schematic representation of a metamorphic super cell structure used in calculating the zigzag and deformed armchair interfaces, respectively;

FIG. 6a is a schematic diagram of a quadrilateral phononic crystal formed by the intersection of two types of elastic insulators;

FIG. 6b is a detailed view of the cross center of the quadrilateral phononic crystal of FIG. 6 a;

FIG. 6c is a characteristic frequency spectrum of the quadrilateral phononic crystal of FIG. 6a, wherein points, circles and stars represent the volume state, boundary state and angular state, respectively;

FIG. 6d is an enlarged partial view of the dashed box in FIG. 6 c;

FIG. 6e is the elastic wave displacement field distribution diagram of two-dimensional volume state, the frequency is 67.57 MHz;

FIG. 6f is a diagram of an elastic wave displacement field distribution of a one-dimensional boundary state, with a frequency of 71.167 MHz;

FIG. 6g is a diagram of an elastic wave displacement field distribution in a zero-dimensional angular state, with a frequency of 78.31 MHz;

FIG. 7a is a schematic diagram of introducing a twisted and bent structure in a quadrilateral phononic crystal;

FIG. 7b is a characteristic frequency spectrum of a tetragonal phononic crystal having a defect structure;

FIG. 8a is a schematic diagram of a two-port bandpass filter based on a 0D angular state;

FIG. 8b is the transmission spectrum of a two-port bandpass filter based on the 0D angular state;

FIG. 8c is the transmission spectrum around the 0D angular frequency of a dual port bandpass filter based on the 0D angular state;

FIG. 8D is the elastic field distribution of the excitation of 0D angular states in a two-port band-pass filter based on 0D angular states;

FIG. 9a is a schematic diagram of the gate voltage induced on the elastic TI;

FIG. 9b is the relationship between Vg and the frequency of elastic double Dirac points;

figure 9c is a transmission spectrum at different gate voltages around the operating frequency of the high Q band pass filter.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. It should be noted that the embodiments and features of the embodiments in the present application may be arbitrarily combined with each other without conflict.

The inventor finds that: the atomic film (two-dimensional material) not only has excellent mechanical properties, but also has outstanding properties in the aspects of electricity, light, magnetism and the like, so that the properties of the atomic film can be adjusted through electrostatic, photoacoustic or magnetoacoustic coupling, and the atomic film (two-dimensional material) becomes an ideal material for adjustable devices. A photonic crystal (PnC) waveguide made of a two-dimensional material, in particular boron nitride, on a patterned substrate is proposed and experimentally verified. Therefore, by using a 2D (two-dimensional) material fixed on a patterned substrate, an electrically tunable elastic wave topological insulator is achievable in practical applications. In embodiments of the present invention, a two-dimensional material is laid down on a honeycomb patterned substrate to form an elastic wave topological insulator. Due to acoustic impedance mismatch between the suspended 2D material and the rigid substrate, elastic topological boundary states and angular states can be realized in the two-dimensional material, and meanwhile, some functional components such as waveguides in any direction, beam splitters and resonators can be realized. It is noteworthy that the frequencies of all these elastic wave assemblies are electrically tunable due to the electromechanical sensitivity of these 2D materials. For example, a 7.26% shift in operating frequency can be achieved in a two-port high-Q bandpass filter by simply applying a gate voltage of 5V. Such elastic topological materials and related devices can greatly facilitate the development of 2D material-based nanoelectromechanical systems, and may be directly applied in modern wireless communication technologies at radio or microwave frequencies.

As shown in fig. 1a to 1c, an elastic wave topological insulator of the present invention includes: the two-dimensional material layer is tiled on the substrate, a honeycomb lattice pattern is arranged on the surface of the substrate, the two-dimensional material layer comprises a first area in contact with the substrate and a suspended second area, the second area is mismatched with the acoustic impedance between the substrates, and the two-dimensional material layer is constructed into a phononic crystal structure.

Specifically, the substrate of the elastic wave topological insulator structure is a substrate with a surface pattern, and the surface pattern is designed into a honeycomb lattice pattern to provide the periodicity and symmetry of the system in order to form the dirac points. To form a topological insulator, Brillouin zone folds [12,25 ] are introduced in a patterned substrate]This is a widely used method of constructing pseudo spins and further achieving band inversion. The honeycomb lattice pattern is specifically an array composed of hexagonal unit cells, and each unit cell comprises six round holes which are crossed in sequence. The hexagon in fig. 1a represents a unit cell (with a side length of a) and the circles in the unit cell represent overlapping circular holes (with a radius of r). The distance between the center of each circular hole and the center of the unit cell where the circular hole is located, namely the hole center distance, is marked as w, and the distances between the centers of the six circular holes in each unit cell and the centers of the unit cells where the six circular holes are located are equal. This patterned substrate size is fully scalable. In this embodiment, the geometrical parameters of the unit cell may be set to the micrometer scale, where a and r are each

And 4. the following examples.5 μm. Such patterned substrates can be prepared by selective surface etching on a variety of thin film composites or directly etched on single or polycrystalline bodies. Such substrate composites are very widely selected, for example SU-8 polymer on Si, silicon dioxide on sapphire or piezoelectric GaAs on AlGaAs. The present embodiment selects a heavily doped silicon on silicon deposited silicon dioxide substrate as a further numerical analog material for subsequent gate voltage application.

As shown in fig. 1b, a two-dimensional material is laid down on such a surface-patterned substrate to form the entire structure of the elastic wave topological insulator. There are no special requirements in the choice of two-dimensional materials, since the mechanical properties are mainly of interest. In this example, the most common two-dimensional material graphene is selected. According to literature, the density, thickness, Young modulus, Poisson's ratio and internal stress of the graphene are 2.267g/cm respectively³0.335nm, 1TPa, 0.165, 0.65N/m. Now, a complete structural model is created. Obviously, the 2D material can be divided into two regions according to the patterned area, one is the area in contact with the substrate and one is the suspended area, and the suspended area is completely continuous because of the overlap of the circular holes. When a two-dimensional material is in close contact with the substrate, the elastic wave propagates only in the suspended region due to the acoustic impedance mismatch between the suspended 2D material and the rigid substrate. Thus, such a continuous atomically thin two-dimensional material creates a phononic crystal structure.

FIGS. 2 a-2 c are phononic crystal elastic wave dispersion curves of a substrate of an embodiment of an elastic wave topological insulator of the present invention; wherein the distances w from the circular holes to the center of the honeycomb structure in fig. 2 a-2 c are 5.5 μm, 6 μm, and 6.6 μm, respectively. FIG. 2d is a graph of the eigenfrequency of an embodiment of the elastic wave topological insulator of the present invention above and below the bandgap at the Γ point as a function of w; wherein, the line A and the line B in the middle of the figure 2d represent the pattern p (p) respectively_xAnd p_y) And d (d)_xyAnd d_x ² _-y ²) (ii) a The left and right hand image files in fig. 2d show the planar field distributions for the p and d modes at 5.5 μm and 6.6 μm, respectively.

The band structure of the phononic crystal was obtained by analyzing its prestressed eigenfrequency at the thin film mechanics module using COMSOL Multiphysics, as shown in fig. 2 b. At about 68.5MHz, there is an elastic double dirac cone at the f point. Now, this phononic crystal is still a standard honeycomb lattice, which is a dirac-like semimetal in which elastic waves can propagate inside when the distance between the centers of the pores satisfies w ═ a/√ 3 ═ 6 μm. As w increases or decreases, the degeneracy of the dierac cone disappears and consequently an elastic band gap is created, as shown in fig. 2 d. This makes PnC two types of insulators, as the band structures formed by the increase and decrease in w are opposite. For example, in the band structure shown in fig. 2a, where w is 5.5 μm, the phononic crystal generates an elastic bandgap of about 5MHz near the original dirac cone, there are two different types of bulk modes at the high and low frequencies of the bandgap, and these two types of bulk modes are named d-mode and p-mode, respectively, just like the electron spin. The d-mode may be classified as d according to the parity symmetry of their eigenstates about the x-or y-axis_xy and d_x ² _-y ²And p-mode can be divided into p_xAnd p_yThe lattice is referred to as topologically sound. Correspondingly, fig. 2c is an energy band structure with w equal to 6.6 μm, now PnC also has a band gap of 5MHz at the same frequency, but the p and d modes are completely opposite, the lattice being a topologically rather indifferent lattice.

Topological phase transitions can be characterized by a dipole moment P. According to high symmetry point C₂The rotation characteristic, the dipole moment P, can be determined by equation (1).

Wherein etaⁿ(k) Is the characteristic value (+ -1) of the rotation of the n-th energy band at the point of K C2, and the C of the highly symmetrical point of K₂The rotation eigenvalues are identified with ± 1. As with the labels of fig. 3a and 3b, the dipole moments for the three bands of the topologically mediocre lattice (w 5.5 μm) are all 0. In contrast, the topological indifferent lattice (w ═ 6.6 μm) has dipole moments of 1/2,0, and 1/2 for the three bands, respectively. These non-zero dipole moments guaranteeThe existence of topological one-dimensional boundary states. I.e., the bulk energy bands of the two insulators are inverted, a topological phase transition occurs to create a boundary state when the topologically mediocre lattice is in contact with the non-mediocre lattice.

From the above theoretical analysis, in order to verify the existence of one-dimensional boundary states (the main feature of the topological insulator is the body boundary correspondence), an interface is constructed on the two elastic insulators as shown in fig. 4a, and the dashed region box marks the structure of the super cell (super cell) used for calculating the projected energy band. The band structure is shown in fig. 4 b. During calculation, Fourier periodic boundary conditions and fixed boundaries are established in the horizontal and vertical directions, respectively. As can be seen from the projected energy bands, two boundary states of energy bands appear in the previous bulk energy band, each band supporting unidirectional transmission of elastic waves at the interface. These two bands are the so-called spiral boundary states, and the propagation direction of the wave they support will combine with the pseudo-spin they have, i.e. the quantum spin hall effect, which is the boundary characteristic of the topological insulator.

To demonstrate that these boundary states feature spin momentum locking and their excellent performance, several elastic wave prototype devices were demonstrated, including (1) elastic waveguides, (2) elastic beam splitters, (3) coupled waveguide ring resonators, as shown in fig. 4 c-4 e, respectively. Fig. 4 c-4 e elastic function devices made of TI boundaries, fig. 4c arbitrary waveguide, fig. 4d beam splitter, fig. 4e critical coupling waveguide with calculated frequencies 69MHz, 69MHz and 69.893MHz, respectively.

In a waveguide, a broadband elastic wave can be bent through an arbitrary bend angle, for example, 120 ° as shown in the drawing, without backscattering. In the beam splitter, after an elastic wave is incident from the source port, the wave propagates mainly to output ports 1 and 3, but rarely to port 2, because ports 1 and 3 support the same pseudo-rotation +1/2, while port 2 supports the opposite pseudo-rotation-1/2 in the incident direction. In the coupled waveguide ring resonator, at the resonance frequency, the elastic wave entering the ring resonator from the waveguide can be completely confined therein and does not flow out, thereby making the entire system an excellent two-port band-stop filter. These functional devices for elastic waves were not present until the TI theory was established, which fully demonstrates the advantages of TI.

The boundary states of the band gap which are hardly visible have been achieved by the above-described embodiments. However, to form a high-order topology, boundary states with large gaps need to be formed. The high-order topological state, namely the zero-dimensional angular state, is demonstrated in the 2D system through the design of a specific scheme. The specific scheme is realized by increasing the degree of the broken symmetry, and the elastic wave structure can be realized by continuously increasing or reducing the distance from the circular hole to the center of the honeycomb structure.

The distances of the compressed lattice and expanded lattice circular holes to the center of the honeycomb in the boundary state of the previous construction were selected to be 5.5 μm and 6.6 μm, respectively. Where these two values are reduced or increased to 5 μm and 7.2 μm, respectively. Projection bands for zigzag-type and broken armchair-type interfaces are then calculated, as shown in fig. 5a and 5b, respectively. The superlattice structure of zigzag (zigzag-type) and branched armchairs (branched armchair-type) interfaces used in the calculation is shown in FIG. 5 c. Floquet periodic boundary conditions and fixed boundary conditions are used in the calculations.

As shown in fig. 5a and 5b, in the original state of the spiral boundary with only a small gap, a large gap occurs around 72MHz, which is caused by the break in symmetry of the crystal lattice at the interface. Another significant band gap occurs around 78MHz, between the high frequency boundary state and the bulk state. Zero dimensional angular states may occur within these bandgaps. The existence of the angular state can be further characterized by calculating the quadrupole moment, namely topological corner charge (topological corner charge). Due to C_6vPoint group symmetry, dipole moment satisfies

The quadrupole moment can be defined by the dipole moment

Calculated topological insulator corner charges of w 5 μm and 7.2 μm are 0 and 1/2, respectively. These non-zero quadrupole moments demonstrate the existence of zero-dimensional angular states.

It will be shown below how the higher order topology is implemented in the proposed two-dimensional system. Figure 6a shows a tetragonal phononic crystal containing two elastic insulators. The period and geometrical parameters of both insulators were identical except for the value of the hole center distance w, which was 7.2 μm for one and 5 μm for the other. According to fig. 2d, the p/d bands of the two insulators are reversed. Inside the PnC there are four boundaries, divided into two, namely two armchair-type boundaries (boundaries II and IV in the figure) and two modified zigzag-shaped boundaries (boundaries I and III in the figure), in the x and y directions respectively. An enlarged top view of the intersection of these two types of interfaces is shown in fig. 6 b. The projected energy bands of these two types of boundaries are shown in fig. 5a and 5b, respectively. In the original continuous helical boundary state, a band gap appears around 72MHz because the symmetry of the lattice breaks at this boundary. Notably, another bandgap appears around 78MHz between the higher frequency edge and the bulk state. The 0D angular states may occur within these bandgaps, supporting the localization of the elastic waves at the intersection of the two types of different topological boundaries (i.e. at the intersection of the two dashed lines in fig. 6 a).

To verify this, all the eigenstates of the four-sided PnC are calculated and their spectrograms are calculated as shown in fig. 6c and 6 d. By observing the elastic field distributions of these eigenstates, it was found that there are simultaneously 2D bulk states, 1D boundary states and 0D angular states in the 2D system, as shown in fig. 6 e-6 g, respectively. For the bulk and boundary states, elastic waves exist inside and at the boundary of the two elastic insulators and are spectrally continuous. As for the angular state, it is independent, appearing at the cross intersection of two different types of interfaces, and its frequencies are separated, in the band gap between the high frequency boundary state and the bulk state, as shown by the dashed lines around 78MHz in fig. 5a and 5 b.

Topology protection the most prominent feature of the higher-order topology is the immunological nature of the defect. In order to verify this characteristic, defects such as bending and lattice distortion, etc. were introduced in the waveguide of the structured quadrangular phononic crystal, as shown in fig. 7 a. Then, the characteristic frequency of the structural phononic crystal is calculated. From its characteristic frequency spectrum 7b, it can be seen that even if a defect is introduced, the angular state still exists stably, and its corresponding frequency hardly changes.

The zero-dimensional locality of topological angular states can be used to implement some high-Q devices. For example, in optics, a high-Q cavity based on angular state can be used to design ultra-low threshold lasers. In this embodiment, a two-port filter is implemented for the elastic wave using the angular state, as shown in fig. 8 a. In practice, the device requires only that the acoustic source be placed at the left port of the sample as shown in fig. 6a and the receiver be placed at the right port of the sample. The two-port transmission spectrum is calculated and, as shown in fig. 8b, its spectral characteristics are highly consistent with the calculated eigenstates (fig. 6 c). In the frequency range of about 69 to 75.5MHz, the two-port device has good transmission performance due to the presence of boundary states in the I and II interfaces. In the frequency range of about 75.5 to 79MHz, the transmission will be greatly reduced if the system has neither bulk nor edge states in these frequencies. However, due to the presence and excitation of the 0D angular state, a distinct transmission peak occurs at 78.31MHz, as shown in fig. 8D. FIG. 8c shows a refined calculation of the transmission spectrum at this angular position with theoretical Q and Q x f values as high as 8 x 10, respectively⁶And 6.26X 10¹⁴Hz. Although the inherent dissipation is not taken into account in the simulation, in practical cases, high Q values close to the theoretical value are possible.

The most important feature of the elastic TI made of 2D material proposed in this embodiment is its electrical tunability, which is an important goal for achieving convenient electrical tunability, especially for micro-acoustic SAW and BAW devices widely used in today's wireless communication. For the photoacoustic topological insulator, because topological boundary transmission needs to waste a large amount of internal structure area, the realization of adjustable frequency and reconfigurable internal structure is very important, so that the utilization rate of the prepared device can be greatly improved. Since 2D materials generally have electromechanical sensitivity, their mechanical properties can be easily tuned by introducing a gate voltage thereto.

Fig. 9a shows a schematic diagram of the introduction of a gate voltage on an elastic TI device. After applying a voltage on the gate, the 2D material (i.e. the substrate) will be inGraphene in the example) and the substrate (highly doped Si in the present example). After the electric field is formed, the 2D material will be subjected to electrostatic pressure and then bend towards the substrate, resulting in additional strain upon deformation, ultimately changing the characteristics and operating frequency of the TI device. In numerical analysis, the electrostatic pressure P can be introduced directly into the suspension region of the 2D material_esTo simulate the above process. When applying a DC voltage V_gP to which the 2D material is subjected when applied to the gate electrode_esIs composed of

Wherein C is_u，ε₀And D and v are the capacitance per unit area between the 2D material and the gate electrode, the vacuum dielectric constant, the distance between the gate and the 2D material, and the real-time displacement of the suspended 2D material during operation, respectively. Equation (3) indicates that P_esTo be connected with V_gAnd d. Thus, d was set to 200nm (which is a typical value from previous experimental studies of nanomechanical resonators), and V was studied_gThe effect on the characteristic frequency of the device. FIG. 9b shows V_gAnd the frequency of the elastic double dirac point as shown in fig. 2 b. Taking the high-Q filter shown in fig. 8 as an example, all devices need only 5V gate voltage to achieve frequency modulation of about 6 MHz. Fig. 9c shows the transmission spectra at different gate voltages. The operating frequency shift of the device can reach 7.26% under the condition of applying a 5V grid voltage. Since graphene can withstand ultra-high strain, electrostatic frequency tunability up to 400% can even be achieved by applying higher gate voltages and more optimized designs.

The embodiment is based on finite element analysis, provides and demonstrates the elastic wave topological insulator based on the two-dimensional material through numerical simulation, respectively shows a one-dimensional boundary state for the elastic waveguide and a zero-dimensional angle state localized in the two-dimensional material, and derives various functional element components from the elastic waveguide, such as the elastic waveguide, a beam splitter, a high-Q resonator, a band-pass filter and a band-stop filter. It is noteworthy that the operating frequency of these components can be effectively electrically tuned due to the electromechanical sensitivity of the two-dimensional material. For example, in a two-port high-Q bandpass filter based on such elastic TI, a shift of about 7.26% of the operating frequency can be achieved by applying only a gate voltage of 5V. In summary, the proposed elastomeric materials and devices can combine integration, high performance, versatility and electrical tunability, which makes them widely applicable in the future in advanced analog signal processors for mobile communications and highly sensitive detectors for the internet of things.

It should be noted that, although the material used in the present embodiment is graphene on a SiO2/Si substrate, the choice of the two-dimensional material and the substrate material is very wide. From the perspective of device size and operating frequency, such devices can be fabricated with a range of hundreds of microns to tens of nanometers (with corresponding operating frequencies ranging from a few megahertz to tens of gigahertz) based on today's mature micro-nano processing techniques and 2D material growth and transfer techniques. From an adjustability perspective, external light, magnetism, heat, gas, etc. may condition such devices in addition to the electrical conditioning demonstrated by the present embodiment. These advantages greatly increase the possibilities of application of acoustic topological materials and devices in practice. Along this research path, it is critical that the piezoelectric 2D material be used to achieve electrical conduction of elastic waves, making this type of device fully compatible with today's micro-acoustic electronics (e.g., SAW and BAW devices based on interdigital transducers).

The above-described aspects may be implemented individually or in various combinations, and such variations are within the scope of the present invention.

Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, and not to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims

1. An elastic wave topological insulator, comprising: the two-dimensional material layer is tiled on the substrate, a honeycomb lattice pattern is arranged on the surface of the substrate, the two-dimensional material layer comprises a first area in contact with the substrate and a suspended second area, the second area is mismatched with the acoustic impedance between the substrates, and the two-dimensional material layer is constructed into a phononic crystal structure.

2. The elastic wave topological insulator of claim 1, wherein: the honeycomb lattice pattern is an array formed by hexagonal unit cells, each unit cell comprises six circular holes which are sequentially crossed, and the distances between the centers of the six circular holes in each unit cell and the centers of the unit cells in which the six circular holes are located are equal.

3. The elastic wave topological insulator of claim 2, wherein: the honeycomb lattice pattern is a topologically mediocre lattice or a topologically non-mediocre lattice.

4. The elastic wave topological insulator according to claim 3, wherein: the substrate is made of one of the following materials: SU-8 polymer, silicon dioxide, and piezoelectric GaAs.

5. The elastic wave topological insulator according to any one of claims 1 to 4, wherein: the two-dimensional material layer is made of graphene.

6. A functional assembly comprising an elastic wave topological insulator according to any one of claims 1 to 5.

7. The functional assembly of claim 6, wherein: the functional component is a beam splitter.

8. The functional assembly of claim 6, wherein: the functional component is a resonator.

9. The functional assembly of claim 6, wherein: the functional component is a filter.

10. The functional assembly of claim 6, wherein: the functional component is a multiplexer.