Topological Interface States Research Articles

Wave Steering by Relaying Interface States in a Valley-Hall-Derived Photonic Superlattice

Topological notions in physics have become a powerful perspective that leads to the discoveries of topological interface states (TISs). In this work, we present a scheme to achieve negative refraction by leveraging the properties of TISs in a valley photonic crystal (VPC). Due to the chiral characteristics, one type of the TISs deterministically possesses negative dispersion relation, which can cause an obliquely incident wave to undergo a negative lateral shift. By stacking multiple VPC interfaces, the TIS-induced lateral shifts can relay in the transmitted wave towards the far side of incidence. The resultant outgoing wave appears to have undergone negative refraction. This finding is verified in microwave experiments. Our scheme opens new application scenarios for topological systems in bulk wave manipulations.

Numerical and experimental evidence of topological interface state in a periodic acoustic black hole

Although the topological interfaces in periodic acoustic black holes (ABHs) have been theoretically reported, there is no published experimental evidence to support this. In this paper, we present experimental evidence and the mechanism explanation of such phenomenon. Meanwhile, the topological protection features are confirmed by introducing defects and geometrical imperfections. The structure under consideration is composed of uniform parts and ABHs with symmetry, which is a necessary condition of Dirac cone. Different from previous works, we used a hybrid mechanism (local resonant and Bragg scattering effect) to generate the multiple topological interface states, resulting in multiple topological inversion points (TIPs). The experiment results are in good agreements with the numerical prediction. This work opens new possibility for manipulating the TIPs in a certain range, which was proved to achieve subwavelength wave control and flexible tunability.

Local resonator stimulated polarization transition in metamaterials and the formation of topological interface states

Developing the acoustic-elastic analogy of a topological insulator has attracted extensive research attention in recent years. Designs developed in the literature strongly rely on reforming the host structure of a system to achieve topology transition. In this article, an innovative topological metamaterial is presented. Unlike topological phononic crystals, the proposed topological metamaterial has a uniform host structure without any phononic crystal features. The band inversion and polarization transition are achieved by manipulating the design of local resonators. It has been proven that by changing the coupling spring constant of local resonators, the mode topologies at the bound states associated with the band gaps can be converted. Three polarization transition points have been found from the bound evolution analysis, and all of them possess the capability of stimulating topological interface states in the corresponding band gaps. The Zak phase calculations have further ascertained the prediction about the topological interface states. The band structure and transmittance spectrum of a supercell lattice of the proposed topological metamaterial have been examined. The topological interface states, as well as the energy localization effects, have been successfully observed in all the three band gaps. The proposed metamaterial brings the convenience of creating topological interface states by carefully manipulating the local resonators only. The methodology presented in this work is thus of practical significance in transforming existing structures into topological systems without revising them.

Tunable control of subwavelength topological interface modes in locally resonance piezoelectric metamaterials

This paper reports the evidence of the tunable sub-wavelength topological interface state in local resonance piezoelectric metamaterials. An elastic beam serves as the host medium with periodically arranged local resonators and attached piezoelectric layers. Thus, the shunt circuits connected with the piezoelectric layers can easily change the electromechanical stiffness in any unit cell. By inspired the band-folding mechanism, doubling the primitive unit cell generates two Dirac points, whose one lower point falls below the locally resonant bandgap and is in the sub-wavelength region. Then, employing the shunt circuit’s tunability opens band-folding points to develop two bandgaps associated with the Bragg scattering effect. Band inversion and topological transition exist during the negative capacitance parameter variation. Numerical simulations demonstrate interface wave propagation for excitation at the interface frequency in the heterostructure, composted of two media with different topological invariants. With the assistance of the piezoelectric shunting circuit, our proposed design can induce wave localization over multiple frequency bands, which has potential for applications such as signal filters, energy harvesting and vibration isolation. Finally, we investigate the relationship between the interface frequency and capacitance and consider the local resonance effect on topological interface modes.

Generation and Tunability of Supermodes in Tamm Plasmon Topological Superlattices

In this study, we propose and experimentally demonstrate a novel kind of Tamm plasmon topological superlattice (TTS) by engineering Tamm photonic crystals (TPCs) belonging to a different class of topology. Utilizing specifically designed double-layer metasurfaces etching on planar multilayered photonic structures, the TPC that supports the Tamm plasmon photonic bandgap is realized in the visible regime. Through the coupling of topological interface states existing between different TPCs, hybrid topological interface states of Tamm plasmon, called supermodes, are obtained that can be fully described by a tight-binding model. Meanwhile, we can achieve a tunable bandwidth of supermodes via varying the etching depth difference between double-layer metasurfaces. We show that the bandwidth decreases with the increase of etching depth difference, resulting in a nearly flat dispersion of supermodes with strong localization regardless of excitation angles. All the results are experimentally verified by measuring angular-resolved reflectance spectra. The TTS and supermodes proposed here open a new pathway for the manipulation of Tamm plasmons, based on which various promising applications such as integrated photonic devices, optical sensing, and enhancing light-matter interactions can be realized.

Tunability of spin-dependent secondary topological interface states induced in an optical complex superlattice

The past decade has witnessed a booming development of topological photonics, which revolutionizes the methodology for controlling the behavior of light. A gigantic achievement is to engineer robust confined modes localized at interfaces between topologically distinct regions, where the optical context can trigger exotic topological phenomena exclusive to photons. Here, we provide an experimentally flexible approach to engineering topologically induced interface states in the visible regime via a unique design of complex superlattice formed by connecting two component superlattices of distinguished topological phases. Assisted by the intrinsic pseudospin degree due to the splitting between TM and TE polarized modes, we attain a precise manipulation of the spin-dependent topological interface states that can manifest themselves straightforwardly through transmission spectra. More specifically, since these topological localized modes stem from the hybridization of artificial photonic orbitals that are of topological origin as well, they are deemed as a novel topological effect and thus named as the secondary topological interface states. Our work develops an innovative and productive strategy to tune topologically protected localized modes, based on which various applications such as selective local enhancement can be exploited.

Probing Rotated Weyl Physics on Nonlinear Lithium Niobate-on-Insulator Chips.

Topological photonics, featured by stable topological edge states resistant to perturbations, has been utilized to design robust integrated devices. Here, we present a study exploring the intriguing topological rotated Weyl physics in a 3D parameter space based on quaternary waveguide arrays on lithium niobate-on-insulator (LNOI) chips. Unlike previous works that focus on the Fermi arc surface states of a single Weyl structure, we can experimentally construct arbitrary interfaces between two Weyl structures whose orientations can be freely rotated in the synthetic parameter space. This intriguing system was difficult to realize in usual 3D Weyl semimetals due to lattice mismatch. We found whether the interface can host gapless topological interface states or not is determined by the relative rotational directions of the two Weyl structures. In the experiment, we have probed the local characteristics of the TISs through linear optical transmission and nonlinear second harmonic generation. Our study introduces a novel path to explore topological photonics on LNOI chips and various applications in integrated nonlinear and quantum optics.

Tuning of subwavelength topological interface states in locally resonant metastructures with shunted piezoelectric patches

We investigate the propagation behavior of the low-frequency topological interface state of the flexural wave in the locally resonant metastructure and analyze the tunability of the sub-wavelength interface states by the piezoelectric shunting circuit. One homogeneous thin beam is periodically attached with local resonant beams, which connect shunted piezoelectric actuators. The folding band obtained by merging two primitive unit cells into one new element can generate a Dirac point below the low-frequency locally resonant bandgap. This folding point is opened to develop one new bandgap originated from the Bragg scattering effect by breaking the mirror symmetry. Then, topological transitions are demonstrated during the distance variation between two adjacent resonances. The interface state’s existence is further confirmed by using steady and transient analysis of the heterostructure composed of two media with different topological properties. Finally, we show the relationship between the interface frequency and the capacitance ratio and research the influence of the distance parameter on the topological interface state. Because of the tunability of elastic waves by the piezoelectric shunting circuit, our design has potential for applications such as energy harvesters, filters, and physical switches.

Acoustic topological interface states of one dimensional metamaterial propagating through a T-shaped junction

We design a supermolecular structure composed of two identical scatterers with opposite orientations in air. By adjusting the interval between them and rotating them, topological phase transitions occur. The combination of rotational and translational operations provides us with wide scope of interface states and multiple-choice to achieve interface states. Therefore, the interface states must exist at the interface between two sublattices with different topological phases. We investigate the subwavelength interface states propagating through a T-shaped junction theoretically, which consists of three one-dimensional waveguides. The results have promising prospects in developing acoustic double-channel transmission devices based on interface states.

Bi2Se3/Bi2Se3 and TlSe/TlSe junctions: enhanced coupling of topological interface states by intercalation

Based on first-principles calculations, we studied the coupling of topological interface states at the interface of Bi2Se3/Bi2Se3 and TlSe/TlSe junctions. From our calculations, the coupling leads to an energy gap at the Dirac point of topological interface states and the energy gap is an exponential decay function of interface spacing when the interface spacing is large enough. The law of exponential decay may be used to identify the formation of interface states from interface-bulk mixed states. It also suggests that the coupling is caused by quantum tunneling. The coupling of the interface states in TlSe/TlSe can be greatly enhanced by intercalating hexagonal BN, although hexagonal BN is often used as a 2D substrate or insulator. The intercalation of bilayer BN or single atomic Au layer can further enhance the interfacial coupling. Our calculations may be helpful for the application of junctions composed of topological insulators.

Conjugated topological interface-states in coupled ring resonators

The optical properties of topological photonics have attracted much interest recently because its potential applications for robust unidirectional transmission that are immune to scattering at disorder. However, researches on topological series coupled ring resonators (T-SCRR) have been much less discussed. The existence of topological interface-states (TIS) in the T-SCRR is described for the first time in this article. An approach has been developed to achieve this goal via the band structure of dielectric binary ring resonators and the Zak phase of each bandgap. It is found that an ultra-high-Q with complete transmission is obtained by the conjugated topological series coupled ring resonators due to the excitation of conjugated topological interface-states, which is different from those in conventional TIS. Furthermore, the problem of transmission decreases resulting from high-Q increases in the traditional photonic system is significantly improved by this approach. These findings could pave a novel path for developing advanced high-Q filters, optical sensors, switches, resonators, communications and quantum information processors.

Topological ring-cavity laser formed by honeycomb photonic crystals

We clarify theoretically that the topological ring-cavity (TRC) modes propagating along the interface between two honeycomb-type photonic crystals distinct in topology can be exploited for achieving stable single-mode lasing, with the maximal intensity larger than a whispering-gallery-mode counterpart by order of magnitude. Especially, we show that the TRC modes located at the bulk bandgap center benefit maximally from the gain profile since they are most concentrated and uniform along the ring cavity, and that, inheriting from the Dirac-like dispersion of topological interface states, they are separated in frequency from each other and from other photonic modes, both favoring intrinsically single-mode lasing. A TRC mode running in a specific direction with desired orbital angular momentum can be stimulated selectively by injecting circularly polarized light. The TRC laser proposed in the present work can be fabricated by means of advanced semiconductor nanotechnologies, which generates chiral laser beams ideal for novel photonic functions.

One-dimensional planar topological laser

Abstract Topological interface states are formed when two photonic crystals with overlapping band gaps are brought into contact. In this work, we show a planar binary structure with such an interface state in the visible spectral region. Furthermore, we incorporate a thin layer of an active organic material into the structure, providing gain under optical excitation. We observe a transition from fluorescence to lasing under sufficiently strong pump energy density. These results are the first realization of a planar topological laser, based on a topological interface state instead of a cavity like most of other laser devices. We show that the topological nature of the resonance leads to a so-called “topological protection”, i.e. stability against layer thickness variations as long as inversion symmetry is preserved: even for large changes in thickness of layers next to the interface, the resonant state remains relatively stable, enabling design flexibility superior to conventional planar microcavity devices.

Construction of Optical Topological Cavities Using Photonic Crystals

A novel design of the Fabry–Pérot optical cavity is proposed, utilizing both the topological interface state structures and photonic bandgap materials with a controllable reflection phase. A one-to-one correspondence between the traditional Fabry–Pérot cavity and optical topological cavity is found, while the tunable reflection phase of the photonic crystal mirrors provides an extra degree of freedom on cavity mode selection. The relationship between the Zak phase and photonic bandgap provides theoretical guidance to the manipulation of the reflection phase of photonic crystals. The dispersions of interface states with different topology origins are explored. Linear interfacial dispersion emerging in photonic crystals with the valley–spin Hall effect leads to an extra n = 0 cavity mode compared to the Zak phase–induced deterministic interface states with quadratic dispersion. The frequency of the n = 0 cavity mode is not affected by the cavity length, whose quality factor can also be tuned by the thickness of the photonic crystal mirrors. With the recent help of topology photonics in the tuning reflection phase and dispersion relationship, we hope our results can provide more intriguing ideas to construct topological optical devices.

Miniband engineering and topological phase transitions in topological-insulator–normal-insulator superlattices

Periodic stacking of topologically trivial and non-trivial layers with opposite symmetry of the valence and conduction bands induces topological interface states that, in the strong coupling limit, hybridize both across the topological and normal insulator layers. Using band structure engineering, such superlattices can be effectively realized using the IV-VI lead tin chalcogenides. This leads to emergent minibands with a tunable topology as demonstrated both by theory and experiments. The topological minibands are proven by magneto-optical spectroscopy, revealing Landau level transitions both at the center and edges of the artificial superlattice mini Brillouin zone. Their topological character is identified by the topological phase transitions within the minibands observed as a function of temperature. The critical temperature of this transition as well as the miniband gap and miniband width can be precisely controlled by the layer thicknesses and compositions. This witnesses the generation of a new fully tunable quasi-3D topological state that provides a template for realization of magnetic Weyl semimetals and other strongly interacting topological phases.

Parametric amplification of topological interface states in synthetic Andreev bands

A driven-dissipative nonlinear photonic system (e.g. exciton-polaritons) can operate in a gapped superfluid regime. We theoretically demonstrate that the reflection of a linear wave on this superfluid is an analogue of the Andreev reflection of an electron on a superconductor. A normal region surrounded by two superfluids is found to host Andreev-like bound states. These bound states form topological synthetic bands versus the phase difference between the two superfluids. Changing the width of the normal region allows to invert the band topology and to create "interface" states. Instead of demonstrating a linear crossing, synthetic bands are attracted by the non-linear non-Hermitian coupling of bosonic systems which gives rise to a self-amplified strongly occupied topological state.

Flat band assisted topological charge pump in the dice lattice

We comparatively study the possible topological charge pump (TCP) in the Dice lattice by considering two types of time-dependent mass terms of the Dirac electrons, the ${S}_{z}$ and $U$ term, which are taken as the pumping potentials. It is shown that the former ${S}_{z}$ pumping potential preserving the electron-hole symmetry of the system leads to a vanishing charge pump, whereas the later $U$ mass term breaking the electron-hole symmetry can pump out an integer number of charges in a pumping cycle, even the Berry phases of Dirac electrons in both cases are the same vanishing, $\ensuremath{\gamma}=0$. The topological interface state (TIS), due to the flat bands bridging the two pumping regions not from the Dirac-cone bands, can account for the TCP found in the $U$-mass pumping case and oppositely, there is no TIS due to the flat bands in the ${S}_{z}$ pumping case. Our findings imply that the flat band in the Dice lattice may contribute to the electron transport under appropriate settings.

Multiple topological interface states in broadband locally resonant phononic crystals

We design a one-dimensional locally resonant phononic crystal (LRPC) comprised of a substrate beam periodically attached with twin resonators. By alternating the position of the resonators, the bandgap forming mechanisms of the LRPC, namely, the band folding-induced bandgaps (BFBGs) and the locally resonant bandgap (LRBG), are analyzed. A broadband “pseudo-bandgap” formed by the LRBG and BFBG can be achieved. The topological properties of the LRPC are then studied, and it is found that the topological interface states can occur only in the BFBGs but not in the LRBG. By constructing a finite LRPC formed by two PCs with distinct topological properties connecting with each other, we numerically and experimentally demonstrate the existence of multiple topological interface states in the BFBGs. The interface state within the subwavelength regime can be achieved with strong energy localization and is little affected by material damping, while for the interface state at high frequencies, it is shown that damping could considerably weaken the energy localization. This work provides guidelines for the design of low-frequency elastic topological systems.

Abnormal topological refraction into free medium at subwavelength scale in valley phononic crystal plates

In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topological modes, which is found to be solely determined by the relative resonant strength between the scatterers, significantly affects the refraction patterns. More interestingly, the outgoing traveling wave through a zigzag interface becomes evanescent when operating at deep sub-wavelength scale. This is realized by tuning the average resonant strength. We show that the evanescent modes only exist along a particular type of outlet edge, and that they can couple with both topological interface states. We also present two designs of topological functional devices, including an elastic one-way transmission waveguide and a near-ideal monopole/dipole emitter, both based on our phononic structure.

Experimental evidence of selective generation and one-way conversion of parities in valley sonic crystals

Valley pseudo-spin and its associated interface wave transport in sonic crystals has attracted increasing attention from researchers for the potential manipulation of acoustic waves. The topological interface state, projected from a specific valley, is valley-locked, and, thus, renders robust reflection immunity against defects. In this work, we report on the experimental observation of the different parity generations of interface states at two distinct zigzag interfaces. By designing a “C”-shaped domain wall, we experimentally demonstrated the parity generation and selective excitation of interface valley-locked states. Benefiting from different parities of the interface states, one-way valley parity conversion was verified in sonic crystals without breaking the time reversal symmetry. Our findings contribute to the applications in noise control, acoustic communication, and logic processing for topological functional devices with unidirectional responses.