Topological Interface States Research Articles

Active control on topological interface states of elastic wave metamaterials with double coupled chains.

Topological elastic wave metamaterials have shown significant advantages in manipulating wave propagation and realizing localized modes. However, topological properties of most mechanical metamaterials are difficult to change because of structural limitations. This work proposes the elastic wave metamaterials with double coupled chains and active control, in which band inversion and topological interface modes can be achieved by flexibly tuning negative capacitance circuits. Finite element simulations and experiments are performed to demonstrate the topological interface modes, which show good agreements with the theoretical results. This research seeks to provide effective strategies for the design and application of topological elastic wave metamaterials.

Experimental demonstration of position-controllable topological interface states in high-frequency Kitaev topological integrated circuits

Topological integrated circuits are integrated-circuit realizations of topological systems. Here we show an experimental demonstration by taking the case of the Kitaev topological superconductor model. An integrated-circuit implementation enables us to realize high resonant frequency as high as 13GHz. We explicitly observe the spatial profile of a topological edge state. In particular, the topological interface state between a topological segment and a trivial segment is the Majorana-like state. We construct a switchable structure in the integrated circuit, which enables us to control the position of a Majorana-like interface state arbitrarily along a chain. Our results contribute to the development of topological electronics with high frequency integrated circuits.

Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions

We study the nonlinear optical properties of heterojunctions made of graphene nanoribbons (GNRs) consisting of two segments with either the same or different topological properties. By utilizing a quantum mechanical approach that incorporates distant-neighbor interactions, we demonstrate that the presence of topological interface states significantly enhances the second- and third-order nonlinear optical response of GNR heterojunctions that are created by merging two topologically inequivalent GNRs. Specifically, GNR heterojunctions with topological interface states display third-order harmonic hyperpolarizabilities that are more than two orders of magnitude larger than those of their similarly sized counterparts without topological interface states, whereas the second-order harmonic hyperpolarizabilities exhibit a more than ten-fold contrast between heterojunctions with and without topological interface states. Additionally, we find that the topological state at the interface between two topologically distinct GNRs can induce a noticeable red-shift of the quantum plasmon frequency of the heterojunctions. Our results reveal a general and profound connection between the existence of topological states and an enhanced nonlinear optical response of graphene nanostructures and possible other photonic systems.

High-speed electro-optic modulation in topological interface states of a one-dimensional lattice

Electro-optic modulators are key components in data communication, microwave photonics, and quantum photonics. Modulation bandwidth, energy efficiency, and device dimension are crucial metrics of modulators. Here, we provide an important direction for the miniaturization of electro-optic modulators by reporting on ultracompact topological modulators. A topological interface state in a one-dimensional lattice is implemented on a thin-film lithium-niobate integrated platform. Due to the strong optical confinement of the interface state and the peaking enhancement of the electro-optic response, a topological cavity with a size of 1.6 × 140 μm2 enables a large modulation bandwidth of 104 GHz. The first topological modulator exhibits the most compact device size compared to reported LN modulators with bandwidths above 28 GHz, to the best of our knowledge. 100 Gb/s non-return-to-zero and 100 Gb/s four-level pulse amplitude modulation signals are generated. The switching energy is 5.4 fJ/bit, owing to the small electro-optic mode volume and low capacitance. The topological modulator accelerates the response time of topological photonic devices from the microsecond order to the picosecond order and provides an essential foundation for the implementation of large-scale lithium-niobate photonic integrated circuits.

Rainbow trapping for sound waves in one-dimensional topological insulator

Over the recent decade, topological insulators, originating from the condensed matter physics, have resided at the frontier in the field of acoustics owing to their novel topological properties for manipulating robust wave propagation, which have also opened an intriguing landscape for potential applications. At the meantime, gradually slowing down acoustic waves with metamaterials allows temporary storage of sound, leading to the exploration of so-called trapped rainbow. However, most of the current studies are reported in a topological trivial context with complex structures, and it is hitherto still a challenge to obtain the high-efficient acoustic rainbow trapping effect in a straightforward setup. Here, we propose an acoustic gradient topological insulator in the one-dimensional system to realize a highly efficient rainbow trapping device. Based on the acoustic analogous Su–Schrieffer–Heeger model, we tune the eigenfrequencies of the topological interface states through modulating the neck widths of Helmholtz resonators. The experimentally measured pressure spectra clearly show that the proposed structure could tightly trap the broad-band sound waves at the target spatial positions. Our proposal may provide versatile possibilities for the design of topological acoustic devices.

Programmable dual-band acoustic topological insulator with dynamically movable interface states

Topological acoustic interface states in one-dimensional (1D) acoustic topological insulators (ATIs) are zero-dimensional (0D) topological states localized at an interface. Unlike topological edge states that can propagate to deliver information in acoustic waveguides, the 0D topological interface states generally cannot serve as information carriers to deliver information from one location to another due to their intrinsic localization. Here, we design and demonstrate a 1D ATI with a movable interface, enabling the 0D topological acoustic interface states to deliver information from one location to another. The ATI design is based on two types of elemental building blocks—denoted as “1” and “0”—which are programmable. These elements of 1 and 0, when periodically arranged, can form topologically distinct crystals, whose interface hosts acoustic topological interface states in two bandgaps simultaneously. Since these two types of elements can switch from each other with external control, a programmable 1D dual-band ATI can be constructed. By programming coding sequences of 1 and 0 elements, we can observe dynamically movable 0D topological interface states riding on a moving interface along the 1D ATI in both bandgaps. Our work opens an avenue to develop topological acoustic devices with programmable and dynamic functions, which may have a variety of potential applications in the fields of energy trapping, topological pumping, information processing, and sound communication.

Metasurface-guided flexural waves and their manipulations

Elastic metasurfaces, being the subject of much attention and discussion, are first designed by phase modulation and now are also considered as a kind of structures with subwavelength size, e.g., layer structures in 3D space or strip structures in 2D space. However, most of elastic metasurfaces, especially those with phase gradient subunits, cannot support elastic wave propagations along them. In this research, we construct non-resonant metasurfaces with an array of slots in plates and explore a unique form of flexural waves propagating along and decaying exponentially with the increasing of the distance from the metasurfaces, which are called metasurface-guided flexural waves. A theoretical framework is established to solve the dispersion relations of these waves by coupling high-order diffraction and waveguide modes. On the basis of this framework, we design three metasurfaces for rainbow reflection, mode conversion and topological interface state, which are realized and verified by finite element simulations and experiments. Our work provides a new idea for the manipulation of flexural waves in plates, which may have wide potential applications in vibration control, structural health monitoring and acoustic device design.

Angle-insensitive topological interface states in hybrid one-dimensional photonic crystal heterostructures containing all-dielectric metamaterials.

Topological interface states (TISs) in conventional one-dimensional (1D) photonic crystal (PhC) heterostructures strongly shift toward higher frequencies as the incident angle increases. This strong blueshift property of TISs intensively limits the operating angle ranges of TISs. Herein, we design two angle-insensitive photonic bandgaps (PBGs) in two hybrid 1D PhCs containing all-dielectric metamaterials. By cascading these two hybrid 1D PhCs to construct a hybrid 1D PhC heterostructure, we achieve an angle-insensitive TIS under transverse magnetic polarization. Empowered by the angle-insensitive property of the PBGs, the angular tolerance of the TIS reaches 69.65°, which is much higher than those of the TISs in conventional 1D PhC heterostructures. In addition, the angle-insensitive property of the TIS is robust against the layer thickness. Our work provides a viable route to achieving TISs with high angular tolerances and would facilitate the applications of photonic topological states.

Multimode topological interface states in a one-dimensional elastic-wave phononic crystal

The one-dimensional (1D) Su-Schrieffer-Heeger (SSH) model is the simplest way to realize the topological phase transition. The topological interface state (TIS) induced by the Zak phase in the SSH model helps researchers to understand and develop the topological band theory, which has been widely promoted and applied in optics and phononics. In this work, we introduce the impedance matching method into the 1D elastic-wave system with three modes (one pure transverse mode and two quasi-longitudinal/transverse) to realize multimode TISs in the same structure. Superior to Zak phase analysis which only can qualitatively determine the presence of one TIS in the band gaps, the proposed impedance matching method allows us quantitatively to design the frequencies of multimode TISs in our elastic-wave model. Numerical band structures, transmission spectra, and field distributions verify these results. We not only extend the calculation of TIS to more complex multimode systems but also obtain multiband TISs with broader application value.

Photonic-crystal-based high-performance ring resonator using a topological interface state: design and analysis.

We propose a photonic crystal ring resonator for the enhancement of quality factor that supports two-dimensionally bounded topological edge states. Crystal parameters are obtained through finite-difference time-domain numerical simulation to get the enhanced quality factor using the topological properties of the photonic crystal. Topological edge states are created when two regions with dissimilar band topologies come together at an interface and are contained within a slab of dielectric material. These edge states can move along sharp edges without backscattering. The transmission dropout issue arises whenever the quality factor is enhanced in a conventional photonic system and is eliminated remarkably by employing the present approach. Such nanoscale photonic crystal structures promote robust interactions between quantum emitters and photonic edge states.

Topological interface states by energy hopping within power-law variable section waveguides

An energy-hopping one-dimensional acoustical topology within power-law variable section waveguides is proposed in this paper, wherein a topological phase transition results from the energy in the basic unit hopping to the nearby unit, with the same energy mode causing its energy band to first close and then open. This study can achieve improved sound energy at the topological interface state and further regulate sound energy based on enhanced sound energy. The large open hole determines the wide frequency range where the designable topological interface state is constructed and the power law of the curve of the structure can adjust the size of the common forbidden band of the two topological states to further improve the bandwidth. The small open hole regulates the magnitude of the acoustic energy at the topological interface state. This research will provide guidance for designing acoustic devices with different frequencies and different acoustic energy concentrations and realizing engineering applications of other multifunctional acoustic devices.

Topological interface states in deep-subwavelength phononic beams

We propose deep-subwavelength phononic beams capable of supporting topological interface states (TISs) at ultra-low frequencies. The topological phononic beams are designed using unit cells with acoustic black hole (ABH) configurations to obtain the first band gap in a low-frequency range, for which the unit cell size is much smaller than the wavelength of the wave to be controlled. We control the topological phases of the phononic beams by modifying the ABH configuration and breaking the inversion symmetry of unit-cell. Two topologically distinct beams are then connected to produce the TIS in their low band gaps. Numerical and experimental results show that TISs are achieved at low frequencies of 4.3–8.5 Hz using the designed phononic beams whose lattice constants (a) are less than λ/20. The value of a/λ is reduced further by adjusting unit-cell arrays of the phononic beams. Given that topological phononic crystals reported in previous studies usually had lattice constants comparable to or several times smaller than wavelengths, the present work offers the possibility of designing a more compact system for topological states at low frequencies.

Topological ventilated sound switch from acoustic Su-Schrieffer–Heeger model

In the last two decades, the emergence of acoustic metamaterials has offered previously unimaginable possibilities for extraordinary control of sound waves. For example, various extremely light-weight sound attenuation systems based on metamaterials and phononic crystals have been demonstrated. Equipped with reconfigurability, such systems will provide the on-demand controls of the passage or stopping of sound waves and are often called acoustic switches or sound switches. However, so far, no ventilated sound switch has been proposed, which can realize both satisfying sound transmission and ventilation. In this work, we demonstrate a topological ventilated sound switch achieving switchable transmission. This switch is based on the one-dimensional acoustic Su-Schrieffer–Heeger model, which leads to the appearance of the topological interface states, and the sound can be turned on or off with the desired ventilation performance. With only one topological unit, the high transmission ratio (∼20 dB) before and after switch has been demonstrated in both simulations and experiments. It should have potential applications in areas of the acoustic engineering where both specific frequency sound transmission and ventilation are required.

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi2 Te3 Interface.

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe0.55 Se0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. Here superconductivity is reported in monolayer (ML) FeTe1-y Sey (Fe(Te,Se)) grown on Bi2 Te3 by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi2 Te3 heterostructures. For y= 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi2 Te3 TIS and the desired spin-momentum locking is not observed. In contrast, for y= 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi2 Te3 system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

Topological energy harvesting of surface acoustic waves in a phononic crystal slab with periodic stubbed surface

In this paper, we demonstrate energy harvesting of surface acoustic waves (SAWs) via topological interface states in a two-dimensional phononic crystal (PC) with the periodic arrangement of bar-like locally resonant units on its surface. The system can produce pure SAW bands in the subwavelength realm due to bar oscillation. Both transverse and longitudinal vibrations of the stubbed bar can selectively couple to the intrinsic SAWs in the PC slab. Subsequently, through constructing the typical Su–Schrieffer–Heeger model, we analyze the topological properties of zone-folding-induced SAW bands with transverse and longitudinal vibration characteristics, respectively. When two arrays with distinct topological bandgaps are spliced together, topological interface states will appear. Topological energy harvesting of SAWs with two different vibration characteristics is finally achieved in one structure. Our study expands the applicability of topological interface states for SAW in a compacted platform, such as polarization selection or sensing.

Robust elastic wave transport in zone-folding induced topological hierarchical metamaterials

The topologically protected elastic wave transport in hierarchical metamaterials for the in-plane mode and out-of-plane mode is investigated in this work. First of all, the influence of two key parameters (the hierarchical order and length ratio) on dispersion relation is studied in detail. It can be found that the introduction of structural hierarchy is beneficial for the formation of low-frequency Dirac cones (DCs). But the number of DCs is independent of the hierarchical order. Moreover, the frequency of DCs and band gaps can be tuned effectively by the length ratio. Tuning the lower-order length ratio is more effective to form low-frequency DCs. Based on above findings, we proposed novel topological hierarchical metamaterials analogue to quantum spin Hall effects (QSHEs) by zone-folding method. By shrinking or expanding the supercell, two types of supercells with distinct topological property are built. In addition, through the dispersion analysis and full-field numerical simulation, topological interface states for both wave modes are obtained successfully, and the robustness is verified also. To overcome the limited frequency range of topological interface states, we try to introduce the temperature-sensitive epoxy into the topological hierarchical metamaterial. Fortunately, the frequency of topological interface states can be tuned in a wide range, and the energy concentration cannot be affected by the temperature. This work will broaden the applied range of hierarchical metamaterials, and is expected to meet the tremendous needs for multifunctional materials in engineering practice.

Tunable Topological Lasing of Circularly Polarized Light in a Soft‐Matter‐Based Superlattice

AbstractThe advance of topological photonics has heralded a revolution for manipulating light as well as for the development of novel photonic devices such as topological insulator lasers. Here, the robust topological interface state lasing in a polymer‐cholesteric liquid crystal superlattice at the visible regime is demonstrated. By use of the femtosecond‐laser direct‐writing and self‐assembling techniques, the micron‐sized superlattice is established with a controlled mini‐band structure and a topological interface defect, thereby achieving a low threshold for robust topological lasing at about 0.4 µJ (722 W·mm−2). Thanks to the chiral liquid crystal, not only is the circularly polarized lasing readily achieved, but the emission wavelength is thermally tuned. The results bring about the possibility to realize tunable, circularly polarized, compact, and integrated topological photonic devices at low cost, as well as to engineer an ideal platform for exploring topological physics that involves light–matter interaction in soft‐matter environments.

Topological rainbow trapping and acoustic energy amplification in two-dimensional gradient phononic crystals

In this work, we numerically and experimentally investigate topological rainbow trapping and energy amplification of acoustic waves in a gradient phononic crystal (PC) structure. Thanks to the acoustic valley Hall effect, topological interface states (TISs) are generated along the interface between two PCs with different topological phases. To achieve rainbow trapping, we introduce the gradient into a 3D-printed PC structure by varying the geometrical parameter of scatterers along the interface. The incident acoustic waves at different frequencies split, stop, and, hence, are significantly amplified at different positions. Notably, the rainbow trapping of TISs is immune to random structural disorders. The topological rainbow trapping is promising for the design of broadband energy harvesters with excellent robustness.

Perfect light absorber with a PT phase transition via coupled topological interface states

Recently, the concepts of parity–time (PT) symmetry and band topology have inspired many novel ideas for light manipulation in their respective directions. Here we propose and demonstrate a perfect light absorber with a PT phase transition via coupled topological interface states (TISs), which combines the two concepts in a one-dimensional photonic crystal heterostructure. By fine tuning the coupling between TISs, the PT phase transition is revealed by the evolution of absorption spectra in both ideal and non-ideal PT symmetry cases. Especially, in the ideal case, a perfect light absorber at an exceptional point with unidirectional invisibility is numerically obtained. In the non-ideal case, a perfect light absorber in a broken phase is experimentally realized, which verifies the possibility of tailoring non-Hermiticity by engineering the coupling. Our work paves the way for novel effects and functional devices from the exceptional point of coupled TISs, such as a unidirectional light absorber and exceptional-point sensor.

Coupling of topological interface states in 1D photonic crystal

Coupling of topological interface states in a one dimensional photonic crystal has been systematically investigated in a broad energy region of electromagnetic spectrum. The robust topological interface states appear when the Zak phase between the adjoining photonic crystals are different at their common photonic bandgap. The coupled interface states created combining three photonic crystals are useful for the spatial confinement and enhancement of electric fields, which could find potential applications in nonlinear photonics and multichannel filters. Anticrossing observed in the dispersion confirms the strong coupling between the topological interface states and causes Rabi-like splitting between them. The splitting energy is found decreasing with increasing number of unit cells in the photonic crystal. The angular and polarization dependency of the coupled states are studied in detail. The resonant wavelength position and bandwidth of the dual reflectivity dips corresponding to the coupled interface states are polarization sensitive and tunable with varying angle of incidence of light.