Topological Interface States Research Articles

Subwavelength topological interface modes in a multilayered vibroacoustic metamaterial

We present a systematic and rigorous analytical approach, based on the transfer matrix methodology, to study the existence, evolution, and robustness of subwavelength topological interface states in practical multilayered vibroacoustic phononic lattices. These lattices, composed of membrane-air cavity unit cells, exhibit complex band structures with various bandgaps, including Bragg, band-splitting induced, local resonance, and plasma bandgaps. Focusing on the challenging low-frequency range and assuming axisymmetric modes, we show that topological interface states are confined to Bragg-like band-splitting induced bandgaps. Unlike the Su-Schrieffer-Heeger model, the vibroacoustic lattice exhibits diverse topological phase transitions across infinite bands, enabling broadband, multi-frequency vibroacoustics in the subwavelength regime. We establish three criteria for the existence of these states: the Zak phase, surface impedance, and a new reflection coefficient concept, all derived from transfer matrix components. Notably, we provide an explicit expression for the exact location of topological interface states within the band structure, offering insight for their predictive implementation. We confirm the robustness of these states against structural variations and identify delocalization as bandgaps narrow. Our work provides a complete and exact analytical characterization of topological interface states, demonstrating the effectiveness of the transfer matrix method. Beyond its analytical depth, our approach provides a useful framework and design tool for topological phononic lattices, advancing applications such as efficient sound filters, waveguides, noise control, and acoustic sensors in the subwavelength regime. Its versatility extends beyond the vibroacoustic systems, encompassing a broader range of phononic and photonic crystals with repetitive inversion-symmetric unit cells.

Topological elastic wave transport and manipulation in three-dimensional metamaterials stacked with sandwich plates

Topological metamaterials demonstrate unprecedented wave manipulation abilities with topologically protected robustness, which have been extensively investigated in one-dimensional (1D) and two-dimensional (2D) mechanical systems, but less explored in three-dimensional (3D) systems. In this study, a 3D topological mechanical metamaterial with periodically stacked sandwich metamaterial plates is proposed to achieve 2D topological surface wave transport in a relatively low-frequency range. An innovative chiral compression-torsion coupling core is employed on the sandwich metamaterial plate to lower the band frequency. Analogous to the quantum valley Hall effect, the two-fold topological nodal line is lifted by breaking the spatial inversion symmetry, opening a topological band gap. By supercell analysis, the topological interface state is demonstrated to appear at the interface of two topologically different domains, and the topological boundary state can also be excited under appropriate free or fixed boundary conditions. Taking advantage of the 3D periodicity, the wave propagation based on both topological interface states and boundary states is examined in both 2D flat plates and 3D structures, realizing 1D topological waveguide and 2D topological surface wave transport respectively. It is found that mode symmetry matching is crucial for constructing the topological wave transport with both interface and boundary states. Leveraging the dependence of boundary states on boundary conditions, this work innovatively presents route-switchable and layer-selective wave manipulation by controlling boundary conditions without complicated structure design, enriching the strategies for tunable elastic wave manipulation. Besides, the topologically protected surface wave transport is demonstrated by introducing defects and disorders. These findings provide new insights into the topological transport of elastic waves in 3D mechanical metamaterials and contribute to the development of intelligent and robust devices for various purposes, such as vibration mitigation, energy harvesting, and signal sensing.

Nonlinear LiNbO3 topological Tamm interface state photonic crystal with static visible and intelligent laser protection

The rapid advancement of high-energy laser and LiDAR technologies imposes heightened demands on intelligent laser protection windows. Traditional laser protection devices often face difficulty in simultaneously achieving high absorption of low-energy laser and high reflection of high-energy laser. Herein, we investigate the efficacy of one-dimensional nonlinear LiNbO3 topological Tamm interface state photonic crystal for static visible and intelligent laser protection applications. The photonic crystal's intelligent laser protection property arises from the amplification of nonlinear effects facilitated by the intense electric field localization surrounding the LiNbO3 interface. At 1064 nm laser energy levels below 18.29 mJ/cm2, the protection window exhibits up to 87.03% absorption. When the laser energy increased to 83.84 mJ/cm2, the reflectance reaches 88.07% attributed to the unsatisfied amplitude matching condition caused by the LiNbO3 nonlinear effect, thereby achieving successful intelligent laser protection. Furthermore, the fabricated sample demonstrates a maximum transmittance of 47.51% in the visible wavelength range. This research provides novel insights into the development of multifunctional advanced optical elements.

Topological interface and corner states of flexural waves in metamaterial plates with glide-symmetric holes

This study investigates the topological localization and propagation of flexural waves in metamaterial plates with perforated holes exhibiting glide symmetry. The dispersion relations of flexural waves in this mechanical system exhibit four-fold Dirac degeneracies at the M point of the Brillouin zone. By properly adjusting the rotation angles of the perforated holes, these degeneracies can be lifted up to create omnidirectional bandgaps, enabling nontrivial topological phases. Both numerical and experimental results demonstrate multiple topological states of flexural waves in the developed elastic metaplates, including dual-band helical interface states and anisotropic interface/corner states. The simple perforated metaplates with glide-symmetric holes provide novel, manufacturable platforms for the flexible manipulation of topological flexural waves, greatly facilitating potential applications such as energy harvesting and signal enhancement.

Topological interface states in deep-subwavelength phononic beams with acoustic black hole configurations

We present deep-subwavelength phononic beams engineered with unit cells incorporating acoustic black hole (ABH) configurations. The ABH design enables the realization of topological interface states (TISs) within the first band gap at low frequencies, where the lattice constant (a) is far smaller than the wavelength (λ) of the controlled wave. Manipulating the ABH configuration and breaking the unit-cell symmetry allow us to control Zak phases for the topological beams. Two topologically distinct phononic beams are interconnected to produce the TIS within their low-frequency band gaps. Through numerical and experimental demonstrations, we confirm the existence of TISs at frequencies ranging from 4.3 to 8.5 Hz using the designed topological beams of which a/λ is less than 1/20. We also offer the potential to further reduce the value of a/λ by rearranging the ABH unit cells.

Flexural edge waves and customizable local modes of circular plates with metasurface

In this research, we study the propagation of flexural edge waves of circular plates (also known as circular-edge waves), present design strategies of metasurfaces for manipulating these waves, and realize customizable edge modes on the basis of edge wave manipulations. Theoretical frameworks are presented to solve the dispersion relationship of circular-edge waves propagating along different boundaries, including a free edge, a strip with a weakness stiffness, and a metasurface with a slot array. On the basis of these frameworks, the propagation characteristics of circular-edge waves are revealed, and the rainbow reflection and topological interface state are realized by constructing metasurfaces. Furthermore, the modal frequency prediction, the robustness to structural parameters, and the effective excitation position for circular-edge modes are explored. Finally, based on the above analysis, the customizable local modes are presented, which means that the position of high energy regions in mode shapes can be designed without changing the corresponding modal frequency. Our work provides a new idea for the manipulation of flexural waves in circular plates and find a potential correlation between flexural waves and vibrations, which may exhibit wide applications in vibration control and acoustic device development.

Realization of topological Bragg and locally resonant interface states in one-dimensional metamaterial beam-resonator-foundation system

Abstract In this study, the one-dimensional (1D) metamaterial beam-foundation system is innovatively improved into a metamaterial beam-resonator-foundation system by inserting resonators into the elastic foundation for ultra-low frequency vibration attenuation and enhanced topological energy trapping. Abundant band gap characteristics are obtained including quasi-static band gap starting from 0 Hz, Bragg scattering band gaps (BSBGs), and local resonance band gaps (LRBGs). Five band folding points are obtained through the band folding mechanism which can be opened by tuning inner and outer resonance parameters. However, only three band folding induced band gaps support mode inversion and Zak phase transition, including one BSBG and two LRBGs. The topological inversion in LRBGs is rarely reported in the 1D mechanical system, which can induce topological locally resonant interface states. The underlying physical mechanism of the topological phase transition in LRBG is revealed, which results from the topological inversion band gap transition from an initial BSBG to a LRBG with resonance parameters changes. Different from conventional 1D topological metamaterials that merely utilize local resonance to lower the band frequency and achieve subwavelength topological states in BSBGs, the topological interface states in LRBGs can localize wave energy to fewer unit cells near the interface, exhibiting enhanced energy localization capacity. The topologically protected interface states are validated with defective cases, demonstrating the potential of topological metamaterials for robust energy harvesting. This study provides new insights into the topological theory of 1D mechanical systems and contributes to the development and implementation of multi-functional devices integrating vibration attenuation and energy trapping.

Photonic crystal topological interface state modulation for nonvolatile optical switching

Phase change materials (PCMs), characterized by high optical contrast (Δn>1), nonvolatility (zero static power consumption), and quick phase change speed (∼ns), provide new opportunities for building low-power and highly integrated photonic tunable devices. Optical integrated devices based on PCMs, such as optical switches and optical routers, have demonstrated significant advantages in terms of modulation energy consumption and integration. In this paper, we theoretically verify the solution for a highly integrated nonvolatile optical switch based on the modulation of the topological interface state (TIS) in the quasi-one-dimensional photonic crystal (quasi-1D PC). The TIS exciting wavelength changes with the crystalline level of the PCM. The extinction ratio (ER) of the topological optical switch is over 18 dB with a modulation length of 9 μm. Meanwhile, the insertion loss (IL) can be controlled within 2 dB. Furthermore, we have analyzed the impact of fabrication errors on the device’s performance. The obtained results show that, the topological optical switch, which changes its “on/off” state by modulating TIS, exhibits enhanced robustness to the fabrication process. We provide an interesting and highly integrated scheme for designing the on-chip nonvolatile optical switch. It offers great potential for designing highly integrated on-chip optical switch arrays and nonvolatile optical neural networks.

Nonadiabatic nonlinear non-Hermitian quantized pumping

We analyze a quantized pumping in a nonlinear non-Hermitian photonic system with nonadiabatic driving. The photonic system is made of a waveguide array, where the distances between adjacent waveguides are modulated. It is described by the Su-Schrieffer-Heeger model together with a saturated nonlinear gain term and a linear loss term. A topological interface state between the topological and the trivial phases is stabilized by the combination of a saturated nonlinear gain term and a linear loss term. We study the pumping of the topological interface state. We define the transfer-speed ratio ω/Ω by the ratio of the pumping speed ω of the center of mass of the wave packet to the driving speed Ω of the topological interface. It is quantized topologically as ω/Ω=1 in the adiabatic limit. It remains to be quantized dynamically unless the driving is not too fast even in the nonadiabatic regime. On the other hand, the wave packet collapses and there is no quantized pumping when the driving is too fast. In addition, the stability against disorder is more enhanced by stronger nonlinearity. Published by the American Physical Society 2024

Highly Tunable Light Absorber Based on Topological Interface Mode Excitation of Optical Tamm State.

Optical absorbers based on Tamm plasmon states are known for their simple structure and high operational efficiency. However, these absorbers often have limited absorption channels, and it is challenging to continuously adjust their light absorption rates. Here, we propose a Tamm plasmon state optical absorber composed of a layered stack structure consisting of one-dimensional topological photonic crystals and graphene nano-composite materials. Using the four-by-four transfer matrix method, we investigate the structural relationship of the absorber. Our results reveal that topological interface states (TISs) effectively excite the optical Tamm state (OTS), leading to multiple absorption peaks. This expands the number of absorption channels, with the coupling number of the TIS determining the transmission quality of these channels-a value further adjustable by the period number of the photonic crystals. Tuning the filling factor, refractive index, and thickness of the graphene nano-composite material allows for a wide range of control over the device's absorption rate, from 0 to 1. Additionally, adjusting the defect layer thickness, incident angle, and Fermi energy enables us to control the absorber's operational bandwidth and the switching of its absorption effect. This work presents a new approach to expanding the tunability of optoelectronic devices.

The Nested Topological Band-Gap Structure for the Periodic Domain Walls in a Photonic Super-Lattice

We study the nested topological band-gap structure of one-dimensional (1D) photonic super-lattices. One cell of the super-lattice is composed of two kinds of photonic crystals (PhCs) with different topologies so that there is a domain wall (DW) state at the interface between the two PhCs. We find that the coupling of periodic DWs could form a new band-gap structure inside the original gap. The new band-gap structure could be topologically nontrivial, and a topological phase transition can occur if the structural or material parameters of the PhCs are tuned. Theoretically, we prove that the Hamiltonian of such coupled DWs can be reduced to the simple Su–Schrieffer–Heeger (SSH) model. Then, if two super-lattices carrying different topological phases are attached, a new topological interface state can occur at the interface between the two super-lattices. Finally, we find the nested topological band-gap structure in two-dimensional (2D) photonic super-lattices. Consequently, such nested topological structures can widely exist in complex super-lattices. Our work improves the topological study of photonic super-lattices and provides a new way to realize topological interface states and topological phase transitions in 1D and 2D photonic super-lattices. Topological interface states in super-lattices are sensitive to frequency and have high accuracy, which is desired for high-performance filters and high-finesse cavities.

Engineering Topological States in Nanographenes

Our research focuses on the rational design, deterministic assembly, and detailed investigation of the physical phenomena emerging from quantum confinement effects in graphene nanomaterials. We pursue a highly integrated multidisciplinary program, founded on synthetic bottom-up approaches toward functional materials with precisely defined structure. We control their assembly into hierarchically ordered architectures and evaluate inherent physical properties using modern scanning probe techniques cross multiple length, time, and energy scales. We recently demonstrated the rational design and experimental realization of a graphene nanoribbon (GNR) superlattices that hosts a 1D array of symmetry-protected topological states, thus generating otherwise inaccessible electronic structure.1 This new class of materials can be thought of as an extended form of poly-acetylene wherein highly localized half-filled topological states replace the familiar single occupied p-orbitals along a conjugated π-system. Experimental results and first-principles calculations reveal that the frontier band structure of these GNR superlattices is defined purely by the coupling between adjacent topological interface states and can be tuned all the way from a semiconductor and a metal.2,3 This novel manifestation of 1D topological phases presents an entirely new route to band engineering in 1D materials based on precise control of their electronic topology and is a promising new platform for future studies of 1D quantum spin physics and metallicity in low dimensional carbon nanomaterials. 1. Topological Band Engineering of Graphene Nanoribbons. Rizzo, D. J.; Veber, G.; Cao, T.; Bronner, C.; Chen, T.; Zhao, F.; Rodriguez, H.; Louie, S. G.; Crommie, M. F.; Fischer, F. R. Nature 2018, 560, 204-206. 2. Inducing Metallicity in Graphene Nanoribbons via Zero-Mode Superlattices. Rizzo, D. J.; Veber, G.; Jiang, J.; McCurdy, R.; Cao, T.; Bronner, C.; Chen, T.; Louie, S. G.; Fischer, F. R.; Crommie, M. F. Science 2020, 369, 1597-1603. 3. Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons. McCurdy, R. D.; Delgado, A.; Jiang, J.; Zhu, J.; Wen, E. C. H.; Blackwell, R. E.; Veber, G. C.; Wang, S.; Louie, S. G.; Fischer, F. R. J. Am. Chem. Soc. 2023, 145, 15162-15170.

Photonic crystal-based high performance cascaded micro ring resonator using topological interface state: design, analysis, and application

Photonic crystal-based high performance cascaded micro ring resonator using topological interface state: design, analysis, and application

Heterostructure channel designs for the topological interface state of surface water waves using topology optimization

The increase of the concentrated density of wave energy is conducive to improving the generation efficiency of wave power generation. Interface states induced in the heterostructure channels can be applied to concentrate the surface water wave. The optimal designs of heterostructure channels can be found through the topology optimization based on the multiple population genetic algorithm to induce a topological interface state with high transmission at the desired frequency. The introduction of the topological interface state effectively and steadily increases the wave energy density in a certain space and improves the robustness and the localization of the water wave concentrator. This topology optimization method provides a design scheme for the wave energy concentrator in the field of ocean engineering.

Topological Rainbow Trapping of Plate‐Mode Waves Based on 1D Gradual Phononic Crystal Slabs

In this article, the concept of topological rainbow is introduced into the plate‐mode waves system of 1D phononic crystal slabs, achieving adjustable topological elastic rainbow trapping by employing gradient‐tuned Su–Schrieffer–Heeger (SSH) structures. First, based on the classical SSH model, a phononic crystal slab composed of steel and aluminum is set up, and the band structure of plate‐mode waves is studied using the finite‐element method. Band inversion can be induced by changing the height of the steel in the unit cell, leading to topological phase transitions. Then, phononic crystals with different topological properties are connected to form a phononic crystal slab, realizing topological interface states. Furthermore, a sandwich‐like ultrathin structure is constructed to couple the adjacent two topological interface states. Finally, a 1D alternating SSH structure of phononic crystal slab is designed under gradient structural parameters, and based on eigenfrequency and full‐wave simulation, adjustable topological rainbow trapping based on coupled interface states is achieved. The designed device can trap wide frequencies exceeding 15 kHz, providing more possibilities for the design of elastic‐energy‐harvesting devices.

Composite photonic lattice with a broad channel to sustain topological interface states.

In the field of topological photonics, one goal is to seek specialized structures with topological protection that can support the stable propagation of light. We have designed a topological configuration featuring a broad channel to sustain edge or interface states. The topological properties are elucidated by analyzing the energy spectrum, eigenstates, and winding numbers. Furthermore, the propagation characteristics of light within our structure are examined through the computation of intensities derived from the coupled mode equations. Our findings reveal that the structure is capable of confining light to the central region, facilitating stable and robust propagation for large-sized beams. Additionally, simulations conducted using commercial software have substantiated the theoretical analysis. Our finding may have significant implications for the modulation of structured light and the development of photonic devices with wide channel capabilities.

Controlling the TE-TM splitting of topological photonic interface states by precise incident angle adjustment

Topological phases in photonic systems have garnered significant attention, often relying on precise structural design for generating non-trivial topological phases. However, this dependency on fixed structures limits their adaptability. This study systematically explores incident angle-induced topological phase transitions in a one-dimensional photonic crystal (PC). Both TE and TM polarized modes undergo topological phase transitions at the same critical transition angles. Additionally, the TM-polarized mode undergoes a unique topological phase transition at the Brewster angle. When these two kinds of transition angles coincide, even if the band structure of the TM-polarized mode undergoes an open-close-reopen process, the topological properties of the corresponding bandgap remain unchanged. Based on theoretical analysis, we design the composite PCs comprising two interfaced PCs having common bandgaps but different topological properties. By tuning the incident angle, we theoretically and experimentally achieve TE-TM splitting of topological interface states in the visible region, which may have potential applications in optical communications, optical switching, photonic integrated circuits, and so on.

Robust high capacity in-plane elastic wave transport in 2D chiral metastructures

Novel 2D tri-chiral metastructures with mass inclusion are proposed in this work. Compared to conventional 2D honeycomb metastructures, these superior metastructures have a wide in-plane low-frequency bandgap (BG) and single Dirac cone (DC) simultaneously. Ligament width and inclusion density are both key factors for tuning the DC and low-frequency BGs. Due to the superior dispersion properties, metamolecules analog of quantum spin Hall effects (QSHEs) are built by the band folding method, and topological phase transition is obtained by shrinking/expanding distance between the mass inclusion and metamolecule center. Topological interface states (TISs) are observed between the two domains with distinct topological properties. To further enhance energy capacity of in-plane elastic wave transport, a 2D heterostructure is constructed by doping waveguiding layer at the topological interface. As expected, robust high capacity in-plane elastic wave transport is realized, named as topological waveguide states (TWSs). While TWS velocity remains unaffected, an increasing number of waveguiding layers additionally leads to a reduced bandgap width and transition from TWSs to conventional edge states (CESs). Average transmitted energy is also observed to increase almost linearly with the thickness of waveguide layer. By virtue of the robust high-capacity wave transport, two potential applications for energy focusing and beam splitting are clearly demonstrated. Besides, the temperature field is introduced into the 2D topological heterostructure to widen the operating frequency of TWSs. Fortunately, TWSs can be tuned to the lower frequency range by increasing temperature, and retain gapless and high-capacity characteristics. Last but not least, we demonstrate that temperature can be used as a switch for in-plane topological wave transport. The proposed 2D chiral metastructures have great potentials to serve as building blocks for multifunctional topological devices.

Experimental demonstration of an electroacoustic transistor

We experimentally demonstrate a topologically protected electroacoustic transistor. We construct a reconfigurable phononic analog of the quantum valley-Hall insulator composed of electrically shunted piezoelectric disks bonded to a patterned plate forming a monolithic structure. The device can be dynamically reconfigured to host one or more topological interface states via breaking inversion symmetry through selective powering of shunt circuits. Above a threshold, the amplitude of wave energy at a chosen location in one topological interface creates a second interface by dynamically switching power between two groups of shunts using relays. This enables the flow of wave energy between two locations in the reconfigured interface analogous to the voltage-controlled electron flow in a field effect transistor. The amplitude of wave energy in the second interface is used for bit abstraction to implement acoustic logic. We illustrate the various states of the transistor and experimentally demonstrate wave-based switching. The proposed electroacoustic transistor is envisioned to find applications in wave-based devices and edge computing in extreme environments and inspire novel technologies leveraging acoustic logic.

Localized thermal emission from topological interfaces.

The control of thermal radiation by shaping its spatial and spectral emission characteristics plays a key role in many areas of science and engineering. Conventional approaches to tailoring thermal emission using metamaterials are hampered both by the limited spatial resolution of the required subwavelength material structures and by the materials' strong absorption in the infrared. In this work, we demonstrate an approach based on the concept of topology. By changing a single parameter of a multilayer coating, we were able to control the reflection topology of a surface, with the critical point of zero reflection being topologically protected. The boundaries between subcritical and supercritical spatial domains host topological interface states with near-unity thermal emissivity. These topological concepts enable unconventional manipulation of thermal light for applications in thermal management and thermal camouflage.