Valley Hall Edge States Research Articles

Elastic wave demultiplexer with frequency dependent topological valley Hall edge states

Valley Hall topological insulators (VHTIs) hold great promise for enhancing the manipulation of elastic wave propagation by their intrinsic topologically protected mechanism. Different from most of VHTIs designed by the deterministic Dirac degeneracy, a more flexible design of VHTIs is proposed by the accidental Dirac degeneracy to steer elastic wave propagation. Based on the accidental Dirac degeneracy, a kind of hexagonal phononic crystal is designed to independently control the topological phase transitions at different frequency ranges. Consequently, a two-channel topological demultiplexer is designed with the function of frequency separation for flexural waves, and its effectivity is verified by numerical simulations and experimental testing. Comparing with traditional designs of demultiplexers, the VHTIs-based demultiplexer possesses a series of advantages in robust performance, easy fabrication and low energy leakage, and sheds light on developing new generation of elastic wave devices.

Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states

Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states

Hybrid topological photonic crystals

Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.

Realization of Topological Valley Hall Edge States of Elastic Waves in Phononic Crystals Based on Material Differences

In this study, the topological valley Hall edge states of elastic waves in phononic crystals are realized based on material differences. A phononic crystal structure with lantern rings is proposed. The results show that differences in the Young's modulus or density of lantern-ring materials can cause the destruction of the effective spatial inversion symmetry, which causes the valley Hall phase transition; thus, topological edge states emerge at the interface of two domains with topologically dissimilar phases. For valley topological transport, the traditional method to break the spatial inversion symmetry is by changing the dimensional parameters of scatterers in phononic crystals. However, in many cases, the space between scatterers is extremely small, making it difficult to obtain a sufficiently large band gap. Moreover, it is difficult to change the transport path and operating-frequency range of elastic waves after sample fabrication is finished. Here, the above problems are solved by the realization of valley topological transport based on changes to lantern-ring materials. The waveguide path is reconfigurable, that is, it can be altered conveniently, and the operating frequency can be tuned by changing the lantern-ring materials. These factors are very important for the topological transport of elastic waves. Topological valley transport achieved by this method has a good backscattering-suppression ability and obvious robustness to defects. Realization of topological valley Hall edge states by utilizing material differences provides an effective method for obtaining the topological transport of elastic waves, breaking the limitations of those based only on structural parameter changes, and this has good application prospects in elastic wave manipulation and communication.

Field-Effect Tunneling between Quantum Valley Hall Edge States and Topological Transistors Based on Bilayer Graphene

We study the tunneling effect between quantum valley Hall edge states under an applied electric field in bilayer graphene containing gaps. A topological transistor based on this tunneling effect is proposed. In the on state of the transistor, the quantum valley Hall edge state along one bilayer-graphene zigzag edge can tunnel to the other edge under an electric field. In the off state without the electric field, the edge state cannot tunnel to the other edge and should be reflected by the top armchair edge and retrace the route along the same zigzag edge. The performance of the transistor is shown to be robust against long-range impurities. Compared with the previous transistor based on quantum spin Hall edge states [Xu et al. Phys. Rev. Lett. 123, 206801 (2019)], this transistor based on quantum valley Hall edge states has the advantages that it does not need a ferromagnetic gate to bridge the gap in the edge states and the conductance is robust against both nonmagnetic and magnetic impurities.

Topological Valley Transport of Elastic Waves Based on Periodic Triangular-Lattices

Topological transports of elastic waves have attracted much attention because of their unique immunity to defects and backscattering-suppression ability. Periodic lattice structures are ideal carriers of elastic-wave transports due to their ability to manipulate elastic waves. Compared with honeycomb-lattice structures, the wave-guide-path designs of triangular-lattice structures have higher flexibility. In this paper, topological transports of elastic waves in the periodic triangular-lattice structure are explored. It is shown that differences between intra-coupling and inter-coupling radii can cause the destruction of the effective spatial inversion symmetry, which gives rise to the valley Hall phase transition and the forming of topological edge states. Utilizing valley Hall effect, topological transports of elastic waves traveling along linear and Z-shaped waveguides are realized with low scattering and immunity to defects. On this basis, the path-selection function of transports of elastic waves in periodic triangular-lattice structures is obtained. Topological valley Hall edge states of elastic waves in periodic triangular-lattice structures have a good application prospects in elastic-wave manipulations and communications.

Gigahertz topological valley Hall effect in nanoelectromechanical phononic crystals

Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented sensitivity and spatial resolution. The valley Hall edge states, protected by band topology, are vividly seen in both real- and momentum-space. The robust valley-polarized transport is evident from the wave transmission across local disorder and around sharp corners, as well as the power distribution into multiple edge channels. Our work paves the way to exploit topological physics in integrated acousto-electronic systems for classical and quantum information processing in the microwave regime.

Valley Hall edge solitons in a photonic graphene.

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Nonlinear topological valley Hall edge states arising from type-II Dirac cones

Type-II Dirac/Weyl points, although impermissible in particle physics due to Lorentz covariance, were uncovered in condensed matter physics, driven by fundamental interest and intriguing applications of topological materials. Recently, there has been a surge of exploration of such generic points using various engineered platforms including photonic crystals, waveguide arrays, metasurfaces, magnetized plasma and polariton micropillars, aiming towards relativistic quantum emulation and understanding of exotic topological phenomena. Such endeavors, however, have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials. Here, we demonstrate nonlinear valley Hall edge states (VHESs) in laser-writing anisotropic photonic lattices hosting type-II Dirac points. These self-trapped VHESs, manifested as topological gap quasi-solitons, are fundamentally distinct from their linear counterparts in type-I lattices and from all previously found topological solitons. Our finding may provide a route for understanding nonlinear phenomena in Lorentz-violating topological systems and for developing advanced light sources from topological insulator lasers.

Observation of topological valley Hall edge states in honeycomb lattices of superconducting microwave resonators

We have designed honeycomb lattices for microwave photons with a frequency imbalance between the two sites in the unit cell. This imbalance is the equivalent of a mass term that breaks the lattice inversion symmetry. At the interface between two lattices with opposite imbalance, we observe topological valley edge states. By imaging the spatial dependence of the modes along the interface, we obtain their dispersion relation that we compare to the predictions of an ab initio tight-binding model describing our microwave photonic lattices.

Interface-dependent tunable elastic interface states in soft metamaterials

Elastic interface states, which are usually generated at the interface of two connected domains with opposite topological invariant, have been successfully demonstrated in periodic structures. Therefore, the interface states determined by the position of interface between two domain walls in one-dimensional elastic systems are rarely reported, which were mainly restricted by the mirror-symmetric geometry of the unit cell. Jointing interface-dependent interface states were mostly implemented with analogs of quantum valley Hall effects in two-dimensional systems. Herein, we first observe two types of elastic interface states simultaneously occurred in one-dimensional combined metamaterials, where two interface modes separately located at two connected domain walls and they can be actively tuned simply through deforming two components on two sides. Flexible and versatile frequency shift and switch on–off characteristics of combination of two interface modes are demonstrated, which may be employed in the multifunctional elastic wave filters, tunable energy harvesting, and elastography devices. Our primitive cell of the soft metamaterial, which breaks the inversion symmetry along the horizontal direction, may be generalized to realize tunable elastic valley Hall edge states.

Phonon manipulation with valley-Hall junctions

In this work, we investigate experimentally the existence of in-plane valley Hall edge states in hexagonal lattices with relaxed space inversion symmetry and we exploit them to realize non-trivial backscattering-free interfaces. We propose special tessellations of lattice domains in which multiple non-trivial domain walls coalesce to form junctions, and we study how guided waves behave when they impinge on such junctions. We show that, through a proper selection of the interface types and orientations, it is possible to achieve junctions with different and exotic wave manipulation capabilities. Specifically, we discuss two applications. The first is a direction-selective splitter, which endows its host lattice with asymmetric wave transport characteristics. The second is a signal delayer that is realized by embedding in the lattice a non-trivial waveguide loop, along which the energy can be temporarily trapped and periodically released. These junctions can serve as building blocks for a new structural logic paradigm enabled by topological mechanics.

Topological Valley Hall Edge State Lasing

AbstractTopological lasers based on topologically protected edge states exhibit unique features and enhanced robustness of operation in comparison with conventional lasers, even in the presence of disorder, edge deformation, or local defects. Here a new class of topological lasers arising from the valley Hall edge states is proposed, which does not rely on magnetic fields. Specifically, topological lasing occurs at domain walls between two honeycomb waveguide arrays with broken spatial inversion symmetry. Two types of valley Hall edge lasing modes are found by shaping the gain landscape along the domain walls. In the presence of uniform losses and two‐photon absorption, the lasing results in the formation of stable nonlinear dissipative excitations localized on the edge of the structure, even if it has complex geometry and even if it is finite. Robustness of lasing edge states is demonstrated in both periodic and finite structures, where such states can circumvent certain corners without scattering losses or radiation into the bulk, as long as the intervalley scattering is absent. The photonic structure and mechanism proposed here for topological lasing is fundamentally different from those previously employed in topological lasers, and can be used for fabrication of practical topological lasers of various geometries.

Rabi-like oscillation of photonic topological valley Hall edge states.

We investigate Rabi-like oscillations of topological valley Hall edge states by introducing two zigzag domain walls in an inversion-symmetry-breaking honeycomb photonic lattice. Such resonant oscillations are stimulated by weak periodic modulation of the lattice depth along the propagation direction that does not affect the overall symmetry and the band topology of the lattice. Oscillations are accompanied by periodic switching between edge states with the same Bloch momentum but located at different domain walls. Switching period and efficiency are the non-monotonic functions of the Bloch momentum in the Brillouin zone. We discuss how the efficiency of this resonant process depends on the detuning of modulation frequency from the resonant value. Switching of nonlinear edge states is also briefly discussed. Our work brings about an effective approach to accomplish resonant oscillations of the valley Hall edge states in time-reversal-invariant topological insulators.

Design and experimental validation on acoustic valley Hall edge states in reconfigurable phononic elastic waveguides

We report on the design and experimental validation of a tunable topological elastic lattice capable of supporting guided waves that are robust against back-scattering from disorder and defects. The topological lattice consists in a patterned aluminum thin plate having through-holes arranged in a hexagonal periodic configuration. The occurrence of the topological edge state is attributed to the acoustic analogue of the electron quantum valley Hall effect. By connecting two lattices having broken space inversion symmetry due to the application of opposite tunable strain fields, a topological transition emerges at the domain wall (i.e., the interface between them). Such a domain wall supports the formation and propagation of quasi-unidirectional edge states. The experimental validation of the topological waveguide is conducted on an aluminum plate that is already fabricated in a deformed (i.e., broken symmetry) configuration. The results confirm the existence of quasi-unidirectional edge states traveling along the domain wall and robust against sharp corners back-scattering. The experimental results also confirm the presence of mechanical energy flux vortices within the unit cell that are used to investigate the origin of the edge states robustness against disorder.