A fractional topological elastic information storage device

Abstract

The present invention discloses a fractional topological elastic information storage device, which is an n-dimensional structure composed of a plurality of disk-folded line structures, each disk-folded line structure is the same, the current disk-folded line structure includes a first disk and a second disk, a first Z-shaped connecting rod and a second Z-shaped connecting rod, the right side of the first disk and the left side of the second disk are connected by the first Z-shaped connecting rod; the right side of the second disk and the first disk of the next disk-folded line structure are connected by the second Z-shaped connecting rod. Not only can the energy storage rate of traditional elastic information devices be effectively improved, but also a solution can be provided for the design of new elastic information signal processing devices.

Description

Technical Field

[0001] The present invention belongs to the technical field of metamaterials, and in particular relates to a fractional topological elastic information storage device. Background Art

[0002] In traditional elastic information storage materials, improving the energy storage rate of the system has always been the focus of researchers. However, due to processing precision errors and interference from environmental disturbances, most energy signals are scattered by defects in energy storage devices. Therefore, the low energy storage rate has always been a difficult problem to be solved in elastic information storage devices. In 2016, three British and American scientists theoretically discovered topological phase transitions and topological phase matter. There are multiple stable topological states in the material, each of which has non-trivial edge modes and exhibits topological protection. In view of this, the theory of topological phase transitions has been widely extended from condensed matter physics to the design of storage devices. For conventional topological information storage devices, the preparation of the device and the construction of the measurement device often have certain difficulties, and the measurement process also has the risk of changing the stored information and the disadvantage of requiring a large basic measurement accuracy. Summary of the invention

[0003] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a fractional topological elastic information storage device.

[0004] Technical solution: The present invention provides a fractional topological elastic information storage device, which is an n-dimensional structure composed of a plurality of disk-fold line structures, each disk-fold line structure is the same, the current disk-fold line structure includes a first disk and a second disk, a first Z-shaped connecting rod and a second Z-shaped connecting rod, the right side of the first disk and the left side of the second disk are connected by the first Z-shaped connecting rod; the right side of the second disk is connected to the first disk of the next disk-fold line structure by the second Z-shaped connecting rod.

[0005] Furthermore, the first disk and the second disk are equal in size; the width of the first Z-shaped connecting rod is w1, the width of the second Z-shaped connecting rod is w2, and w1≠w2;

[0006] Furthermore, a finite element solver is used to perform full-wave simulation to calculate the energy state distribution characteristics of the device, and free boundary conditions are set during the calculation process.

[0007] Furthermore, the free boundary condition is to use an elastic band to vertically suspend the fractional topological elastic information storage device on a rigid bracket.

[0008] Furthermore, a continuous laser probe is used to measure the vibration displacement u of the center point of the disk of the disk-broken line structure during the excitation process, and the distribution of the local state density of the disk-broken line structure is obtained based on the displacement and the Purcell effect.

[0009] Furthermore, the fractional charge value Q in each cell of the device is calculated using the following formula: ω :

[0010]

[0011] Among them, ω gap is the preset upper limit, unit p represents the total number of disks in the disk-polyline structure in the unit cell, ρ i (ω) represents the local density of states of the i-th disk in the unit cell.

[0012] Furthermore, when the information storage device is a one-dimensional structure, the horizontal distance L1 between the first disk and the second disk is 49.9 mm, the horizontal distance L2 between the second disk and the first disk in the next disk-fold line structure is 50.4 mm, the width w1 of the first Z-shaped connecting rod is 1.3 mm, the width w2 of the second Z-shaped connecting rod is 2.1 mm, the radii of the first disk and the second disk are both 15 mm, the thicknesses of the first disk and the second disk are both 1.75 mm, and the Z-shaped connecting rod deviates from the center line by 5 mm, and the center line is a horizontal line formed by connecting the centers of the two disks.

[0013] Furthermore, when the information storage device is a two-dimensional structure, the horizontal distance L1 between the first disk and the second disk is 50.8 mm, the horizontal distance L2 between the second disk and the first disk in the next disk-fold line structure is 50 mm, the width w1 of the first Z-type connecting rod is 2 mm, the width w2 of the second Z-type connecting rod is 1.1 mm, the radii of the first disk and the second disk are both 15 mm, the thicknesses of the first disk and the second disk are both 1.8 mm, and the Z-type connecting rod deviates from the center line by 5 mm, and the center line is the horizontal line formed by connecting the centers of the two disks.

[0014] Furthermore, a disclination-type two-dimensional structure fractional topological elastic information storage device is constructed by the following method:

[0015] Step 1: Set the cell in the hth row and the gth column: align the first disk-fold line structure and the second disk-fold line structure in the two horizontal directions up and down, and the disks in the first disk-fold line structure and the second disk-fold line structure also form a disk-fold line structure in the vertical direction through the first and second Z-shaped connecting rods, h = 1, 2, ..., H, g = 1, 2, ..., G; H represents the total number of rows, and G represents the total number of columns;

[0016] Step 2: The cell in the hth row and the gth column is connected to the cell in the hth row and the g+1th column through the second Z-shaped connecting rods in the two disk-broken line structures in the horizontal direction, and the cell in the hth row and the gth column is connected to the cell in the h+1th row and the gth column through the second Z-shaped connecting rods in the two disk-broken line structures in the vertical direction;

[0017] Step 3: Get a lattice with H rows and G columns, cut off 1 / 4 of the upper right corner of the entire lattice, and then splice the gap. If H is an odd number, the center point of the spliced ​​lattice is located in a cell. If H is an even number, the center point of the spliced ​​lattice is located at the junction of the cells.

[0018] Step 4: Adjust the fractional topological elastic information storage device of the spliced ​​two-dimensional structure so that the lengths of all the first Z-shaped connecting rods are equal and the lengths of all the second Z-shaped connecting rods are equal.

[0019] Beneficial effects: The present invention aims to optimize the structural design of traditional elastic information storage devices through the SSH (Su-Schrieffer-Heeger) model in condensed matter physics, improve the energy storage rate of traditional elastic information storage devices and accurately control the distribution of elastic information state density from the perspective of physical principles. The present invention can obtain surface displacement signals through continuous laser detectors. Topological states can be propagated without being affected by device processing, so that signals can be stored and transmitted in various complex environments. It can not only effectively improve the energy storage rate of traditional elastic information devices, but also provide solutions for the design of new elastic information signal processing devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the disc-fold line structure of the present invention;

[0021] Figure 2 is the fractional topological charge map in the 1D SSH model of the present invention;

[0022] Figure 3 It is a construction diagram of the 1D SSH model of the present invention;

[0023] Figure 4 It is an experimental diagram of the 1D SSH model of the present invention;

[0024] Figure 5 A construction diagram of a 2D disclination model with an odd number of unit cell columns according to the present invention;

[0025] Figure 6 This is an experimental diagram of a 2D disclination model with an odd number of unit cell columns of the present invention;

[0026] Figure 7 This is a diagram for constructing a 2D disclination model of the present invention in which the number of unit cell columns is an even number. DETAILED DESCRIPTION

[0027] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0028] The present invention cleverly uses the controllable properties of metamaterials to construct a one-dimensional and two-dimensional topological phase system based on the SSH model to optimize the structural design of traditional elastic information storage devices, with the aim of improving the energy storage rate of traditional elastic information devices through structural optimization.

[0029] Due to the unique controllable properties in elastic metamaterials, in order to further explore the topological behavior in elastic metamaterials, the one-dimensional SSH (Su-Schrieffer-Heeger) model in condensed matter physics is introduced as a theoretical framework to create an elastic information storage system with coexisting topological phases. Through the combination of experimental characterization and numerical simulation, this embodiment demonstrates the existence of stable topological states and their state density distribution in adjustable metamaterials. It can stably store elastic information. The research results of this embodiment emphasize the application prospects of adjustable elastic metamaterials from energy collection to information processing.

[0030] The SSH model describes elastic waves propagating through a periodic lattice of a set of coupled mechanical oscillators. By deriving the Hamiltonian in matrix form, the interatomic coupling strength and phase differences between adjacent oscillators are considered to establish the conditions for opening and closing the energy gap. These conditions determine the emergence of topological states in the metamaterial.

[0031] The tight binding model for the bistable lattice in this embodiment is an extension of the one-dimensional SSH model, and its Hamiltonian is as follows:

[0032]

[0033] H stands for Hamiltonian. In the SSH model, a primitive cell consists of two different lattice points (A and B). For a model with a total of N primitive cells, n is the primitive cell number. t1 and t2 are two different coupling sizes between the two lattice points, and Hc represents Hermitian conjugation.

[0034] The bulk topology of the one-dimensional SSH model mentioned above can be characterized by polarization, expressed as:

[0035]

[0036] p represents the polarization intensity, u k represents the wave vector of the model in k-space, Represents the partial derivative with respect to k, and dk is the amount of change in the integral. This formula calculates the product of the inner product of the band wave function and the wave vector derivative for each wave vector k in the Brillouin zone and integrates it over the entire Brillouin zone. This produces a topological invariant, the topological polarization. The result of the topological polarization is a quantized value that is not zero in the presence of boundary states. It is used to characterize the topological phase of the system, such as the case of topological insulators and topological metals.

[0037] In the experiment, the fractional charge is calculated by the local density of states ρ related to the distribution of topological states in the frequency and spatial domains. i (ω) obtained by integration:

[0038]

[0039] Among them, Q ω is the calculated fractional charge, ρ i (ω) refers to the local state density at the i-th lattice point in the unit p, and the frequency ω gap is the upper frequency limit of the integral, representing the cutoff frequency in the band gap, and dω is the change in frequency during the integral. The fractional charge is the accumulation of the local state density at all positions in the primitive cell p (unitp), which corresponds to the imaginary part of the Green function:

[0040]

[0041] Among them, for a system composed of N atoms, the Green's function It has the form of a tensor, which comes from the normalized biorthogonal right Hamiltonian corresponding to the jth state of the system and left Eigenvector. ω refers to frequency, and is the eigenvalue corresponding to the jth state, i refers to the imaginary unit, η j is the loss coefficient corresponding to the j-th state.

[0042] A fractional topological elastic information storage device of the present invention is an n-dimensional structure composed of a plurality of disk-folded line structures, such as Figure 1 As shown, each disk-fold line structure is the same. The current disk-fold line structure includes a first disk and a second disk, and a first and a second Z-shaped connecting rod. The right side of the first disk and the left side of the second disk are connected by the first Z-shaped connecting rod; the right side of the second disk is connected to the first disk of the next disk-fold line structure by the second Z-shaped connecting rod.

[0043] The first disk and the second disk are equal in size; the width of the first Z-shaped connecting rod is w1, the width of the second Z-shaped connecting rod is w2, and w1≠w2;

[0044] The finite element solver is used to perform full-wave simulation to calculate the energy state distribution characteristics of the device. In order to ensure the validity of one-dimensional and two-dimensional approximations during the calculation process, free boundary conditions are used around the one-dimensional and two-dimensional devices respectively.

[0045] The free boundary condition is to use an elastic band to vertically suspend the fractional topological elastic information storage device on a rigid bracket, and the contact area between the elastic band and the device should be as small as possible while ensuring that the entire device is not affected by additional forces in the out-of-plane direction.

[0046] In the optical experimental verification, a continuous laser probe was used to detect the out-of-plane elastic information of the lattice points on the one- and two-dimensional periodic chains. A POLYTEC laser vibrometer OFV-5000 with an OFV-505 probe was used, with a bandwidth of 2.5MHz. The sound source was provided by a modal exciter SA-JZ002 with a bandwidth of 15kHz. The vibration displacement of the disk was measured by the laser probe.

[0047] Due to the Purcell effect, the imaginary part of the Green function (corresponding to the local state density) defined on the elastic wave system caused by the excitation of a point source with a constant source intensity Q is proportional to the excited wave function, which corresponds to the displacement u observed at the point source. Therefore, by measuring the displacement at each point source during the excitation process, the distribution of the local state density in the model where the point source is located can be obtained.

[0048] The fractional charge value Q of the device is calculated using the following formula according to formula 3 ω :

[0049]

[0050] Among them, ω gap is the preset upper limit, unit p represents the total number of disks in the disk-polyline structure in the unit cell, ρ i (ω) represents the local density of states of the i-th disk in the unit cell.

[0051] In this embodiment, when the information storage device is a one-dimensional structure, the lattice constant is a=100.03mm, the horizontal distance L1 between the first disk and the second disk is 49.9mm, the horizontal distance L2 between the second disk and the first disk in the next disk-folding line structure is 50.4mm, the width w1 of the first Z-type connecting rod is 1.3mm, the width w2 of the second Z-type connecting rod is 2.1mm, the radius of the first disk and the second disk are both 15mm, the thickness of the first disk and the second disk are both 1.75mm, the Z-type connecting rod deviates from the center line by 5mm, and the center line is a horizontal line formed by connecting the centers of the two disks. Due to the destruction of translational symmetry, an omnidirectional band gap is formed. The band gap range is 16.40kHz to 16.58kHz.

[0052] In this embodiment, when the information storage device is a two-dimensional structure, the horizontal distance L1 between the first disk and the second disk is 50.8 mm, the horizontal distance L2 between the second disk and the first disk in the next disk-fold line structure is 50 mm, the width w1 of the first Z-type connecting rod is 2 mm, the width w2 of the second Z-type connecting rod is 1.1 mm, the radii of the first disk and the second disk are both 15 mm, the thicknesses of the first disk and the second disk are both 1.75 mm, the center line is a horizontal line formed by connecting the centers of the two disks, and the corresponding frequency of the localized state in the band gap is 16.52 kHz.

[0053] Figure 2 is the fractional topological charge in the 1D SSH model of the present invention. The topological charge distribution is related to the ratio between the intracellular coupling r and the intercellular coupling s, as Figure 2 As shown in (a) in Figure 2 As shown in (b), due to the reflection symmetry, the lattice is divided into two parts. There is a charge Q = e / 2 at the boundary of the model, where a filling anomaly occurs. By measuring the displacement at each point source during the excitation process, the corresponding LDOS can be directly obtained. By setting an appropriate upper limit, the fractional topological charge of the corresponding state of the filling anomaly can be obtained, as Figure 2 As shown in (c) in . Figure 2 The light blue region in (c) represents the integration domain below the Fermi level, where the displacement curve is Figure 2 The color of the corresponding position of the point source in (a) is the same. However, when the ratio of the intra-cell coupling coefficient r to the inter-cell coupling coefficient s is far away from the limit 0, the fractional charge localized at the edge gradually diffuses into the body. Figure 2 As shown in (d), in the 1D SSH model, as the r / s ratio changes, the present invention calculates the fractional topological charge of the mth unit.

[0054] Figure 3 This is the construction of the 1D SSH model of the present invention. Figure 3 As shown in (a), tunable disks and different zigzag structures are constructed with certain thicknesses to simulate atoms and their couplings. Figure 3 As shown in (b), in the unit cell simulation with a length of a = L1 + L2, points O and E in the Brillouin zone show parity respectively, so there is parity inversion in the first energy band between them. Figure 2 The finite-size 1D SSH model mentioned in , using the same structural parameters, was constructed as Figure 3 The elastic lattice shown in (c) is shown in Figure 1. The simulated and calculated energy bands are shown in Figure 1. Figure 3 As shown in (d), two edge states appear in the band gap. Figure 3(e) shows the simulated wave functions of the edge states in the band gap, which are localized at both ends of the model.

[0055] Figure 4 This is an experiment of the 1D SSH model of the present invention. In the experimental setup, piezoelectric transducers and reflective stickers (such as Figure 4 As shown in (a) in Figure 4 As shown in (b), the sample is suspended in a suitable position and ensured to be free from vertical external interference. By inputting the chirp signal into the piezoelectric transducer behind the target disk, the displacement signal can be accurately measured using a Polytec OFV-055 laser vibrometer focused on the reflective sticker. The center point of each disk is set as the measurement point, and the displacement u can be measured, which is verified to correspond to the LDOS at each position. By performing Fourier transform on these displacement signals in the frequency domain, the displacement curve is obtained, and then the normalized fractional topological charge of each unit cell is obtained. Part of the measured displacement curve is shown in Figure 4 As shown in (c) in Figure 4 As shown in (d), the experimental results are compared with the theoretical calculations of the 1D SSH model, and the slight diffusion of the edge topological charge can also be seen in this practical model.

[0056] Figure 5 A redesigned lattice is proposed for the construction of the 2D disclination model of the present invention. Figure 5 As shown in (a), the lattice design method is:

[0057] Step 1: Set the cell in the hth row and the gth column: align the first disk-fold line structure and the second disk-fold line structure in the two horizontal directions up and down, and the disks in the first disk-fold line structure and the second disk-fold line structure in the vertical direction constitute a disk-fold line structure in the vertical direction, h = 1, 2, ..., H, g = 1, 2, ..., G; H represents the total number of rows, and G represents the total number of columns;

[0058] Step 2: The cell in the hth row and the gth column is connected to the cell in the hth row and the g+1th column through the second Z-shaped connecting rods in the two disk-broken line structures in the horizontal direction, and the cell in the hth row and the gth column is connected to the cell in the h+1th row and the gth column through the second Z-shaped connecting rods in the two disk-broken line structures in the vertical direction;

[0059] Step 3: Get a lattice with H rows and G columns, cut off 1 / 4 of the upper right corner of the entire lattice, and then splice the gap. Figure 5 If H in is an odd number, the center point of the spliced ​​lattice is located in a unit cell;

[0060] Step 4: Adjust the fractional topological elastic information storage device of the spliced ​​two-dimensional structure so that the lengths of all the first Z-shaped connecting rods are equal and the lengths of all the second Z-shaped connecting rods are equal.

[0061] Figure 5 (b), (c), (d), and (e) show the theoretical lattices of the topological crystalline insulator (TCI) and general insulator (NI) phases, as well as the corresponding plan views of the elastic lattice, respectively.

[0062] Figure 6 This is an experiment of the 2D disclination model of the present invention. Similar to the 1D SSH model, Figure 6 As shown in (a), for both 2D disclination models, piezoelectric sensors and reflective stickers are fixed on the surface of all disks. Figure 6 The measured shifts at representative positions in the TCI phase are shown in (b), corresponding to the energy bands shown in the background. Figure 6 (b) also shows the energy state distribution and representative eigenmodes of the TCI phase, where the corner states are located within the central body band. Figure 6 (c) and Figure 6 (d) shows the comparison between the experimental results and theoretical calculations, where the colored blocks represent the TCI phase and the NI phase, respectively.

[0063] Figure 7 Another 2D disclination model of the present invention is constructed by using steps 1 to 4. Figure 7 As shown in (a), when there is an even number of cells on one side of the initial lattice, the center point of the spliced ​​lattice is located at the center of the cell junction, forming a new disclination structure; similar to the aforementioned TCI phase, Figure 7 As shown in (b) in the figure, the lattice is also redesigned and constructed in the elastic lattice, changing the original coupling to a more parallel and symmetrical structure. Considering the Fermi level covering the valence band, the corresponding Wannier center is Figure 7 Ideally, considering the actual coupling in the model, the fractional charge distribution in each unit cell is as follows: Figure 7 Compared with the theoretical calculation, Figure 7 The simulated energy bands shown in (e) also show good consistency.

[0064] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

Claims

1. A fractional topological elastic information storage device, characterized in that: The information storage device is an n-dimensional structure composed of a plurality of disk-fold line structures, each disk-fold line structure is the same, the current disk-fold line structure includes a first disk and a second disk, a first Z-shaped connecting rod and a second Z-shaped connecting rod, the right side of the first disk and the left side of the second disk are connected by the first Z-shaped connecting rod; the right side of the second disk and the first disk of the next disk-fold line structure are connected by the second Z-shaped connecting rod, and n=1 or 2.

2. A fractional topological elastic information storage device according to claim 1, characterized in that: The first disk and the second disk are equal in size; the width of the first Z-shaped connecting rod is w1, the width of the second Z-shaped connecting rod is w2, and w1≠w2.

3. A fractional topological elastic information storage device according to claim 1, characterized in that: The finite element solver is used to perform full-wave simulation to calculate the energy state distribution characteristics of the device, and free boundary conditions are set during the calculation process.

4. A fractional topological elastic information storage device according to claim 3, characterized in that: The free boundary condition is to use an elastic band to vertically suspend the fractional topological elastic information storage device on a rigid bracket.

5. A fractional topological elastic information storage device according to claim 1, characterized in that: A continuous laser probe is used to measure the vibration displacement u of the center point of the disk of the disk-broken line structure during the excitation process. Based on the displacement and the Purcell effect, the distribution of the local state density of the disk-broken line structure is obtained.

6. A fractional topological elastic information storage device according to claim 1, characterized in that: The fractional charge value Q in each cell of the device is calculated using the following formula: ω : Among them, ω gap is the preset upper limit, unit p represents the total number of disks in the disk-polyline structure in the unit cell, ρ i (ω) represents the local density of states of the i-th disk in the unit cell.

7. A fractional topological elastic information storage device according to claim 1, characterized in that: When the information storage device is a one-dimensional structure, the horizontal distance L1 between the first disk and the second disk is 49.9 mm, the horizontal distance L2 between the second disk and the first disk in the next disk-fold line structure is 50.4 mm, the width w1 of the first Z-shaped connecting rod is 1.3 mm, the width w2 of the second Z-shaped connecting rod is 2.1 mm, the radii of the first disk and the second disk are both 15 mm, the thicknesses of the first disk and the second disk are both 1.75 mm, and the Z-shaped connecting rod deviates from the center line by 5 mm, and the center line is a horizontal line formed by connecting the centers of the two disks.

8. A fractional topological elastic information storage device according to claim 1, characterized in that: When the information storage device is a two-dimensional structure, the horizontal distance L1 between the first disk and the second disk is 50.8 mm, the horizontal distance L2 between the second disk and the first disk in the next disk-fold line structure is 50 mm, the width w1 of the first Z-type connecting rod is 2 mm, the width w2 of the second Z-type connecting rod is 1.1 mm, the radii of the first disk and the second disk are both 15 mm, the thicknesses of the first disk and the second disk are both 1.8 mm, and the Z-type connecting rod deviates from the center line by 5 mm, and the center line is the horizontal line formed by connecting the centers of the two disks.

9. A fractional topological elastic information storage device according to claim 1, characterized in that: The following method is used to construct a disclination-type two-dimensional structural fractional topological elastic information storage device: Step 1: Set the cell in the hth row and the gth column: align the first disk-fold line structure and the second disk-fold line structure in the two horizontal directions up and down, and the disks in the first disk-fold line structure and the second disk-fold line structure also form a disk-fold line structure in the vertical direction through the first and second Z-shaped connecting rods, h = 1, 2, ..., H, g = 1, 2, ..., G; H represents the total number of rows, and G represents the total number of columns; Step 2: The cell in the hth row and the gth column is connected to the cell in the hth row and the g+1th column through the second Z-shaped connecting rods in the two disk-broken line structures in the horizontal direction, and the cell in the hth row and the gth column is connected to the cell in the h+1th row and the gth column through the second Z-shaped connecting rods in the two disk-broken line structures in the vertical direction; Step 3: Get a lattice with H rows and G columns, cut off 1 / 4 of the upper right corner of the entire lattice, and then splice the gap. If H is an odd number, the center point of the spliced ​​lattice is located in a cell. If H is an even number, the center point of the spliced ​​lattice is located at the junction of the cells. Step 4: Adjust the fractional topological elastic information storage device of the spliced ​​two-dimensional structure so that the lengths of all the first Z-shaped connecting rods are equal and the lengths of all the second Z-shaped connecting rods are equal.

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