Quantum Valley Hall Effect Research Articles

Localizing Elastic Edge Waves via the Topological Rainbow Effect

We combine two different fields, topological physics and graded metamaterials, to design a topological metasurface to control and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic plate, using a square lattice, that hosts symmetry-induced topological edge states. By concurrently allowing the elastic substrate to spatially vary in depth, we are able to convert the incident slow wave into a series of robust modes, with differing envelope modulations. This adiabatic transition localizes the incoming energy into a concentrated region where it can then be damped or extracted. For larger transitions, different behavior is observed; the incoming energy propagates along the interface before being partitioned into two disparate chiral beams. This ``topological rainbow'' effect leverages two main concepts, namely the quantum valley Hall effect and the rainbow effect usually associated with electromagnetic metamaterials. The topological rainbow effect transcends specific physical systems; hence, the phenomena we describe can be transposed to other wave physics. Because of the directional tunability of the elastic energy by geometry, our results have potential for applications such as switches, filters, and energy harvesters.

Experimental demonstration of valley-protected backscattering suppression and interlayer topological transport for elastic wave in three-dimensional phononic crystals

Topological insulator (TI) that possesses topologically protected characteristic of guiding the wave against disorders and structural perturbations without backscattering has attracted significant research interest in various fields including electromagnetic, acoustic and elastic system. However, for the mechanical system, realizing an elastic analogue of three-dimensional (3D) TI supporting the topologically protected wave propagation in two-dimensional (2D) plane is still a challenge due to the complicated mode polarization of elastic wave in 3D. This paper theoretically and experimentally investigates the robust and layer-selective transports of elastic wave in 3D monolayer- and bilayer-stacked plate-like metamaterial structures. Firstly, considering 3D monolayer-stacked structure, the 2D valley surface states are achieved numerically along the 2D projected plane based on the mechanism of quantum valley Hall effect. The simulation and experimental measurement are performed to confirm the robust transport of 3D elastic wave and backscattering immunity against the straight channel and sharp bends. Then, by stacking the monolayer into bilayer with a twisted angle of 60°, non-zero interlayer coupling of elastic valley layer is introduced and the layer-related topological phase is revealed in the 3D bilayer-stacked structure, giving rise to the 2D topological layer-dependent surface states. Finally, the 3D robust layer-selective transports of elastic wave are tested by experiment. This research provides exciting application perspectives for ultrasonic devices with robustness, lower-power consumption and high-dimensional manipulation.

Real-time steering of curved sound beams in a feedback-based topological acoustic metamaterial

We present the concept of a feedback-based topological acoustic metamaterial as a tool for realizing autonomous and active guiding of sound beams along arbitrary curved paths in free two-dimensional space. The metamaterial building blocks are acoustic transducers, embedded in a slab waveguide. The transducers generate a desired dispersion profile in closed-loop by processing real-time pressure field measurements through preprogrammed controllers. In particular, the metamaterial can be programmed to exhibit analogies of quantum topological wave phenomena, which enables unconventional and exceptionally robust sound beam guiding. As an example, we realize the quantum valley Hall effect by creating, using a collocated pressure feedback, an alternating acoustic impedance pattern across the waveguide. The pattern is traversed by artificial trajectories of different shapes, which are reconfigurable in real-time. Due to topological protection, the sound waves between the plates remain localized on the trajectories, and do not back-scatter by the sharp corners or imperfections in the design. The feedback-based design can be used to realize arbitrary physical interactions in the metamaterial, including non-local, nonlinear, time-dependent, or non-reciprocal couplings, paving the way to unconventional acoustic wave guiding on the same reprogrammable platform. We then present a non-collocated control algorithm, which mimics another quantum effect, rendering the sound beams uni-directional.

Demonstration of Suppressed Backscattering in Acoustic Valley Hall Topological Insulator

Acoustic topological insulators are at the frontier of acoustic metamatetials research. The analogue of the quantum valley-Hall effect (QVHE) in sound waves has led to acoustic valley Hall topological insulators (VHTIs). Here, we construct a new acoustic VHTI with C3v- symmetric hexagonal cells. The sound propagation along the interface is demonstrated via simulations. By introducing defects along the interface, such as cavity or bendings, we observe the robust transports to these defects in acoustic VHTIs. In addition, we construct several waveguides to quantitatively analyze the suppressed backscattering. The results illustrate that the new designed acoustic VHTIs in this paper possess better backscattering suppression in sound propagation, although the penetration is lower than the previously designed acoustic VTHIs.

Spin-valley locked topological edge states in a staggered chiral photonic crystal

Engineering pseudo-spin and valley degrees of freedom using quantum spin Hall and valley Hall effects has opened up remarkable possibilities for highly efficient and robust signal transport in time-reversal invariant photonic systems. Here we present a spin-valley locked photonic crystal that has distinct signs of chirality of sublattices in a honeycomb unit cell. We show that the photonic crystal has an insulating bulk dispersion and sublattice-dependent spin-valley coupled gapless edge states by exploiting a coupled dipole method and demonstrate valley-selective propagation by controlling spin state of an external dipole source. The interplay between spin, valley and sublattice shows a judicious way for one-way photon transport by using multiple degrees of freedom.

Reconfigurable topologically protected wave propagation in metastable structure

In this paper, topologically protected wave propagation in metastable structure has been investigated by mimicking the quantum valley Hall effect. Reconfigurable topological waveguides are achieved by switching the metastable states of the structure. First, a K-point Dirac cone, which is guaranteed by the C6 rotational symmetry of the metastable unit cell, is identified in the band structure. Then, by reconfiguring the bistable elements, the space inversion symmetry of the unit cell is broken and a topological bandgap opened. The topological non-triviality of this bandgap is verified by the values assumed by the Berry curvature and valley Chern number. Next, the topological edge modes localized at the interface are studied by analyzing the dispersion relation of a finite strip. The analysis results show that reconfigurable topologically protected waveguides, which are immune to backscattering at sharp corners and local defects, can be achieved utilizing the edge modes.

Light-induced irreversible structural phase transition in trilayer graphene

A crystal structure has a profound influence on the physical properties of the corresponding material. By synthesizing crystals with particular symmetries, one can strongly tune their properties, even for the same chemical configuration (compare graphite and diamond, for instance). Even more interesting opportunities arise when the structural phases of crystals can be changed dynamically through external stimulations. Such abilities, though rare, lead to a number of exciting phenomena, such as phase-change memory effects. In the case of trilayer graphene, there are two common stacking configurations (ABA and ABC) that have distinct electronic band structures and exhibit very different behaviors. Domain walls exist in the trilayer graphene with both stacking orders, showing fascinating new physics such as the quantum valley Hall effect. Extensive efforts have been dedicated to the phase engineering of trilayer graphene. However, the manipulation of domain walls to achieve precise control of local structures and properties remains a considerable challenge. Here, we experimentally demonstrate that we can switch from one structural phase to another by laser irradiation, creating domains of different shapes in trilayer graphene. The ability to control the position and orientation of the domain walls leads to fine control of the local structural phases and properties of graphene, offering a simple but effective approach to create artificial two-dimensional materials with designed atomic structures and electronic and optical properties.

Experimental realization of a reconfigurable electroacoustic topological insulator

A substantial challenge in guiding elastic waves is the presence of reflection and scattering at sharp edges, defects, and disorder. Recently, mechanical topological insulators have sought to overcome this challenge by supporting back-scattering resistant wave transmission. In this paper, we propose and experimentally demonstrate a reconfigurable electroacoustic topological insulator exhibiting an analog to the quantum valley Hall effect (QVHE). Using programmable switches, this phononic structure allows for rapid reconfiguration of domain walls and thus the ability to control back-scattering resistant wave propagation along dynamic interfaces for phonons lying in static and finite-frequency regimes. Accordingly, a graphene-like polyactic acid (PLA) layer serves as the host medium, equipped with periodically arranged and bonded piezoelectric (PZT) patches, resulting in two Dirac cones at the K points. The PZT patches are then connected to negative capacitance external circuits to break inversion symmetry and create nontrivial topologically protected bandgaps. As such, topologically protected interface waves are demonstrated numerically and validated experimentally for different predefined trajectories over a broad frequency range.

Elastically-supported lattices for tunable mechanical topological insulators

Emerging mechanical topological insulators based on Quantum Valley Hall Effect (QVHE) offer a myriad of unconventional and robust properties in controlling wave motion. Designing mechanical topological insulators requires a careful assignment of the system’s mechanical properties in a specific manner. Consequently, modulating the topological property of a fabricated system is typically challenging. Here, we introduce an externally adding-on mechanism that enables high tunability of QVHE without the need to alter the main fabricated structure. Specifically, we exploit a periodic elastic foundation to control the topological property of a hexagonal lattice. Non-equal stiffnesses of the elastic foundation break the inversion symmetry of the hexagonal lattice, thus introducing the QVHE to the system. A mathematical framework is established to understand the fundamental mechanism and design the topologically protected waveguides by tuning the elastic foundation. The achieved topological insulators exhibit high tolerance over defects. The paradigm in this work opens promising avenues for mechanical metamaterials with tunable topological properties.

Quantum valley Hall effect in wide-gap semiconductor SiC monolayer

We have investigated the valley Chern number and gapless edge states in wide-gap semiconductor SiC and BN monolayers by using the density functional theory calculations. We found that while SiC monolayer has a non-quantized valley Chern number due to a partial mixing of the Berry curvature peaks pertaining to the opposite valleys, there exist topologically protected gapless edge states within the bulk gap, leading to a quantum valley Hall effect. Doping of the opposite charge carriers causes a backscattering-free valley current flowing on the opposite edge, which can be used for experimental confirmation and application at room temperature. BN monolayer, on the other hand, was found to have gapped edge states due to the too large staggered AB-sublattice potentials.

Nature of topological protection in photonic spin and valley Hall insulators

Recent interest in optical analogues to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method comprehensively characterizes possible 2D hexagonal designs and reveals their topological nature, potential and limits.

Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene

A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report a definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moiré patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic fields can be fine-tuned by both the rotation angle and heterostrain. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.

Locally polarized wave propagation through crystalline metamaterials

Wave propagation control is of fundamental interest in many areas of Physics. It can be achieved with wavelength-scaled photonic crystals, hence avoiding low frequency applications. By contrast, metamaterials are structured on a deep-subwavelength scale, and therefore usually described through homogenization, neglecting the unit-cell structuration. Here, we show with microwaves that, by considering their inherent crystallinity, we can induce wave propagation carrying angular momenta within a subwavelength-scaled collection of wires. Then, inspired by the Quantum Valley-Hall Effect in condensed matter physics, we exploit this bulk circular polarization to create modes propagating along particular interfaces. The latter also carry an edge angular momentum whose conservation during the propagation allows wave routing by design in specific directions. This experimental study not only evidences that crystalline metamaterials are a straightforward tabletop platform to emulate exciting solid-state physics phenomena at the macroscopic scale, but it also opens the door to crystalline polarized subwavelength waveguides.

Gapless unidirectional photonic transport using all-dielectric kagome lattices

Photonic topological insulators are a promising photonic platform due to the possibility of unidirectional edge states with insensitivity to bending, fabrication imperfections or environmental fluctuation. Here we demonstrate highly efficient unidirectional photonic edge mode propagation facilitated by an optical analogue of the quantum valley Hall effect. With an all-dielectric kagome lattice design, we demonstrate broadband suppressed reflection in the presence of sharp corners and further show negligible vertical losses in a semiconductor-based device at telecommunication wavelengths.

Dirac degeneracy and elastic topological valley modes induced by local resonant states

In elastic systems, the current technique to produce Dirac degeneracy is based on Bragg scattering eigenstates, which, however, suffers from operating only at relatively high frequency determined by lattice constant. Here, an elastic metamaterial plate that presents an analog to the quantum valley Hall effect (QVHE) is proposed to achieve Dirac degeneracy with local resonant states, enabling us to tune the operating frequency without altering the lattice. By introducing resonator pair into a hexagonal lattice, a local resonance states-induced Dirac cone is produced right below the local resonant band gap caused by the resonator pair. After gapping the Dirac cone with unequal masses of the resonator pair, a new local resonant band gap supporting topological edge modes immune to backscattering appears. This band gap is formed by mixing effective negative mass effect and Bragg scattering effect due to large virtual mass. These ideas are demonstrated by numerical simulation, as well as validated by the experiment on flexural wave in a textured plate. The proposed design provides a new degree of freedom to control elastic topological mode and paves the way to explore subwavelength elastic topological interface states.

Valley-dependent topologically protected elastic waves using continuous graphene membranes on patterned substrates.

We present a novel structure for topologically protected propagation of mechanical waves in a continuous, elastic membrane using an analog of the quantum valley Hall effect. Our system involves a thin, continuous graphene monolayer lying on a pre-patterned substrate, and as such, it can be employed across multiple length scales ranging from the nano to macroscales. This enables it to support topologically-protected waves at frequencies that can be tuned from the kHz to GHz range by either selective pre-tensioning of the overlaying membrane, or by increasing the lattice parameter of the underlying substrate. We show through numerical simulations that this continuous system is robust against imperfections, is immune to backscattering losses, and supports topologically-protected wave propagation along all available paths and angles. We demonstrate the ability to support topologically-protected interface modes using monolayer graphene, which does not intrinsically support topologically non-trivial elastic waves.

Tunable metallic and topological properties in two-dimensional ligand-functionalized antimonene films

Using first-principle calculations, we predict that fully-hydroxyl-decorated antimonene (SbOH) is a two-dimensional topological insulator with extraordinarily global gap of 330 meV, and incompletely hydroxyl-decorated antimonene films show metallic properties. The ligand OH on top side of SbOH@SiC(1 1 1) heterostructure can be veered by external electric field, which induces a switchable in-plane spontaneous polarization. Moreover, the asymmetry and strong spin-orbit coupling of SbOH leads to spin polarization of edge states and a pair of unequal valleys that have opposite Berry curvatures near the vertices (K and K’) of Brillouin zone. The tunable of valley polarization in SbOH is useful to realize quantum valley Hall effect. In the case, SbOH shows the dual TI with coexisting switchable ferroelectric and valley polarization. Ferroelectric topological materials provide a new paradigm for device engineering, such as perfect-focusing Veselago lens and spin-selective electron collimator. Based on spin polarization of edge states, we suggest a transistor model using the spin direction as a switch. We can tune the material to be metal, TI, or ferroelectric TI according to SbO film partially or completely hydroxylated. Our findings not only broaden the family of the 2D ferroelectric topological materials, but also offer a promising platform for novel electronic and spintronic applications.

Voltage-controlled quantum valley Hall effect in dielectric membrane-type acoustic metamaterials

The research interest on phononic crystals now takes a new turn towards the acoustic/elastic analogies of the quantum concepts, e.g., the quantum Hall, quantum spin Hall and quantum valley Hall effects. One hallmark of these fundamental physical phenomena is the existence of topological edge/interface modes that propagate through the system along a designed path, with high robustness against week disorders. However, the working frequency ranges of the proposed topological phononic systems are usually very narrow, which therefore pose a clear limitation in practical applications. Motivated by this difficulty, we design and study a membrane-type metamaterial with tunable topological properties. The plane wave expansion method is employed to analyze its dispersion relation. A theoretical method is further proposed to conveniently calculate the valley Chern number. The theoretical and numerical results show the existence of topologically protected interface mode in the system. Its frequency range can be changed over a wide range by applying an electrical voltage, while the localization behavior of the interface mode is independent of the controlling operation. Consequently, we have successfully shown that the working frequency range of the topological phononic systems so derived can be significantly `broadened' and hence the practical application may be dramatically widened.

Topological edge states in phononic plates with embedded acoustic black holes

We report on the design of phononic plates based on a periodic lattice of acoustic black holes (ABH) and capable of supporting topological edge states. The design is based on the established concept of the acoustic valley Hall effect (AVHE) that is the elastic analogue of the quantum valley Hall effect (QVHE) for quantum mechanical systems. The basic structure consists of a triangular lattice of circular ABHs whose symmetry guarantees the existence of Dirac dispersion at the corners of the Brillouin zone. Starting from this symmetric lattice, space inversion symmetry (SIS) can be broken by introducing an angle-dependent scaling of the ABH taper profile. Depending on the sign of the scaling factor, two topologically distinct lattice configurations can be obtained and assembled in order to create a domain wall characterized by unconventional dynamic properties. More specifically, such domain wall supports the formation and propagation of quasi-unidirectional elastic guided modes that are topologically protected against back-scattering due to impurities or defects in the lattice.

Topological valley, pseudospin, and pseudospin-valley protected edge states in symmetric pillared phononic crystals

We present a symmetric double-sided pillared phononic crystals (PPnCs) that can emulate both quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE) by solely imposing different geometric perturbations. Indeed, the Dirac cones can occur in the low (deep subwavelength) and high frequency regime by judiciously turning the parameters of the attached pillars and even a double Dirac cone can be achieved. We realize the valley-protected, the pseudospin-protected or the pseudospin-valley coupled edge states with the proposed platform. Besides, we show a variety of refraction phenomena (positive, negative and evanescent) of the valley-polarized edge state at the zigzag termination when emulating QVHE. Further, we illustrate the valley-dependent feature of the pseudospin-valley coupled edge state and demonstrate the valley based splitting of the pseudospin-protected edge states in a Y-junction wave guide.