arXiv subjects

Hai-Xiao Wang

Publications and source records attributed to Hai-Xiao Wang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Classical higher-order topological insulators

Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order topological insulators (HOTIs) have been increasingly explored, featuring lower-dimensional topological boundary states, leading to rich mechanisms for topological manipulation, guiding and trapping of classical waves. Here, we provide an overview of current developments of HOTIs in classical waves including basic principles, unique physical properties, various experimental realizations, novel phenomena and potential applications. Based on these discussions, we remark on the trends and challenges in this field and the impacts of higher-order topology on other research fields.

cond-mat.mtrl-sci↗

arXiv2020

Observation of a phononic higher-order Weyl semimetal

Weyl semimetals are extraordinary systems where exotic phenomena such as Fermi arcs, pseudo-gauge fields and quantum anomalies arise from topological band degeneracy in crystalline solids for electrons and metamaterials for photons and phonons. On the other hand, higher-order topological insulators unveil intriguing multidimensional topological physics beyond the conventional bulk-edge correspondences. However, it is unclear whether higher-order topology can emerge in Weyl semimetals. Here, we report the experimental discovery of higher-order Weyl semimetals in its phononic analog which exhibit topologically-protected boundary states in multiple dimensions. We create the physical realization of the higher-order Weyl semimetal in a chiral phononic crystal with uniaxial screw symmetry. Using near-field spectroscopies, we observe the chiral Fermi arcs on the surfaces and a new type of hinge arc states on the hinge boundaries. These topological boundary arc states link the projections of Weyl points in different dimensions and directions, and hence demonstrate higher-order multidimensional topological physics in Weyl semimetals. Our study establishes the fundamental connection between higher-order topology and Weyl physics in crystalline materials and unveils a new horizon of higher-order topological semimetals where unprecedented materials such as higher-order topological nodal-lines may emerge.

cond-mat.mes-hall↗

arXiv2020

On-chip higher-order topological micromechanical metamaterials

Higher-order topological insulators exhibit multidimensional topological physics and unique application values due to their ability of integrating stable boundary states at multiple dimensions in a single chip. However, for signal-processing applications in high-frequency mechanical systems, the current realizations of higher-order topological mechanical materials are still limited to large-scale systems for kilohertz or lower frequencies. Here, we report the experimental observation of a on-chip micromechanical metamaterial as higher-order topological insulator for high-frequency mechanical waves. The higher-order topological phononic band gap is induced by the band inversion at the Brillouin zone corner which is achieved by configuring the orientations of the elliptic pillars etched on the silicon chip. With consistent experiments and theory, we demonstrate the coexistence of topological edge and corner states in the megahertz frequency regime as induced by the higher-order band topology. The experimental realization of on-chip micromechanical metamaterials with higher-order topology opens a regime for applications based on megahertz mechanical waves in an integrated platform where the edge and corner states act as stable waveguides and resonators, respectively.

physics.app-ph↗

arXiv2020

Higher-Order Weyl Semimetals

Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report the theoretical discovery of higher-order Weyl points and thereby the establishment of such an important connection. We demonstrate that higher-order Weyl points can emerge in chiral materials such as chiral tetragonal crystals as the intermediate phase between the conventional Weyl semimetal and 3D higher-order topological phases. Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases.

cond-mat.mtrl-sci↗

arXiv2020

Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals

The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with $π$-fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux, using 2D sonic crystals with $p4gm$ and $p2gg$ symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate, gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, (iii) quantized Wannier band polarizations in these Wannier sectors. Remarkably, the protective glide symmetries are well-preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering.

cond-mat.str-el↗

arXiv2020

Higher-order topological spin Hall effect of sound

We propose theoretically a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, $C_6$, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit-cell. In the nontrivial phase, the sonic crystal realizes the topological spin Hall effect in a higher-order fashion: (i) The edge states emerging in the bulk band gap exhibits partial spin-momentum locking and are gapped due to the reduced spatial symmetry at the edges. (ii) The gapped edge states, on the other hand, stabilize the topological corner states emerging in the edge band gap. The partial spin-momentum locking is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta, where the pseudospin is emulated by the acoustic orbital angular momentum. We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.

cond-mat.mes-hall↗

arXiv2020

Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry

Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.

cond-mat.mes-hall↗

arXiv2019

Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals

Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond the conventional topological paradigms. Here, we discover experimentally that the nonsymmorphic $p4g$ acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, while the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexing topological phenomena and to reveal a topological transition triggered by the geometry-transition from the $p4g$ group to the $C_{4v}$ group which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates an instance that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions.

cond-mat.mtrl-sci↗

arXiv2019

Valley kink states and topological channel intersections in substrate-integrated photonic circuitry

Valley degrees of freedom, providing a novel way to increase capacity and efficiency of information processing, have become an important instrument for photonics. Experimental studies on photonic topological valley kink states at interfaces between regions with opposite valley-Chern numbers have attracted much attention, however, were restricted to zigzag-type interfaces, largely limiting their applications such as geometry-dependent topological channel intersections. Here, we experimentally demonstrate and manipulate valley kink states at generic interfaces in subwavelength substrate-integrated photonic circuitry. We verify the robustness of the kink states by measuring transmissions of the kink states through twisted interfaces and interfaces with disorders. Based on the valley kink states at generic interfaces, we realize several topological channel intersections where photonic transport paths are related to geometries of the intersections. In comparison to those in previous works, the present valley photonic crystals have subwavelength thicknesses and excellent self-consistent electrical shielding, which are perfectly compatible with conventional substrate-integrated photonic circuitry. Our work opens a door to manipulate photonic valley pseudo-spins in substrate-integrated circuitry with robustness, easy access, and lightweight.

physics.app-ph↗

arXiv2019

Photonic Chern insulators made of gyromagnetic hyperbolic metamaterials

Controlling light propagation using artificial photonic crystals and electromagnetic metamaterials is an important topic in the vibrant field of photonics. Notably, chiral edge states on the surface or at the interface of photonic Chern insulators can be used to make reflection-free waveguides. Here, by both theoretical analysis and electromagnetic simulations, we demonstrate that gyromagnetic hyperbolic metamaterials (GHM) are photonic Chern insulators with superior properties. As a novel mechanism, the simultaneous occurrence of the hyperbolic and gyromagnetic effects in these metamaterials is shown to open the large topological band gaps with gap Chern number of one. Importantly, unlike many other photonic Chern insulators, the GHM Chern insulators possess non-radiative chiral edge modes on their surfaces, and thus allow to fabricate unidirectional waveguides without cladding metals which generally incurr considerable Ohmic loss. Furthermore, the photonic edge states in the proposed Chern insulators are robust against disorder on a wide range of length scales, in strong contrast to crystalline topological insulators, and the light flow direction on the surface of the Chern insulators can be easily flipped by switching the direction of an applied magnetic field. Fascinatingly, we find that negative refraction of the topological surface wave occurs at the boundary between the GHMs with the opposite signs of gyromagnetic parameters. Finally, we show that compared with other photonic topological materials such as chiral hyperbolic materials, the present GHM Chern insulators can be much easier to fabricate.

cond-mat.mes-hall↗

arXiv2019

Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology

The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical calculation of the topological invariants for several photonic/sonic crystals. We demonstrate that these topological photonic/sonic crystals are topological crystalline insulators with fragile topology, a feature which has been ignored in previous studies. We further discuss the bulk-edge correspondence in these systems with emphasis on symmetry broken on the edges.

cond-mat.mes-hall↗

arXiv2018

Second-order photonic topological insulator with corner states

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not been found in photonic systems yet. In this article, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically non-trivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily-fabricated structure of the photonic crystals, we can realize different topological phases with unique topological boundary states straightforwardly. Our result can be generalized to higher dimensions and provides unprecedented venues for higher-order photonic topological insulators and semimetals.

cond-mat.mtrl-sci↗

arXiv2018

Observation of second-order topological insulators in sonic crystals

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization of generalized Berry phases of the bulk energy bands through the bulk-edge correspondence, a paradigm that can also be extended to acoustic and photonic systems. Recently, high-order topological insulators (HOTIs) are proposed and observed, where the bulk topological invariants result in gapped edge states and in-gap corner or hinge states, going beyond the conventional bulk-edge correspondence. However, the existing studies on HOTIs are restricted to tight-binding models which cannot describe the energy bands of conventional sonic/photonic crystals that are due to multiple Bragg scatterings. Here, we report theoretical prediction and experimental observation of acoustic second-order topological insulators (SOTI) in two-dimensional (2D) sonic crystals (SCs) beyond the tight-binding picture. We observe gapped edge states and degenerate in-gap corner states which manifest bulk-edge correspondence in a hierarchy of dimensions. Moreover, topological transitions in both the bulk and edge states can be realized by tuning the angle of the meta-atoms in each unit-cell, leading to various conversion among bulk, edge and corner states. The emergent properties of the acoustic SOTIs open up a new route for topological designs of robust localized acoustic modes as well as topological transfer of acoustic energy between 2D, 1D and 0D modes.

cond-mat.mes-hall↗

arXiv2018

Topological transitions in continuously-deformed photonic crystals

We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the holes and/or the distance between them, multiple transitions between normal and topological photonic band gaps (PBGs) can appear. The time-reversal symmetric topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states. We search for optimal topological transitions, i.e., sharp transitions sensitive to the geometry, and optimal topological PBGs, i.e., large PBGs with clean spectrum of edge states. Such optimizations reveal that dielectric-frame photonic crystals are promising for optical sensors and unidirectional waveguides.

physics.optics↗

arXiv2018

Topological light-trapping on a dislocation

Topology has been revealed to play a fundamental role in physics in the past decades. Topological insulators have unconventional gapless edge states where disorder-induced back-scattering is suppressed. In photonics, such edge states lead to unidirectional waveguides which are useful for integrated photonic chips. Cavity modes, another type of fundamental components in photonic chips, however, are not protected by band topology because of their lower dimensions. Here we demonstrate that concurrent wavevector-space and real-space topology, dubbed as the "dual-topology", can lead to light-trapping in lower-dimensions. The resultant photonic bound state emerges as a Jackiw-Rebbi soliton mode localized on a dislocation in a two-dimensional (2D) photonic crystal, as predicted theoretically and discovered experimentally. Such a strongly-confined 0D localized mode, which is solely due to the topological mechanism, is found to be robust against perturbations. Our study unveils a new mechanism for topological light-trapping in lower-dimensions, which is valuable for fundamental physics and a variety of applications in photonics.

physics.optics↗

arXiv2017

Topological Node-Lines in Mechanical Metacrystals

Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of topological node-lines in three-dimensional mechanical metacrystals with ribbon- or drumhead-like surface states. These two-dimensional topological surface states offer unprecedented, robust subwavelength confinement of elastic waves. Design principles for topological mechanical metamaterials, from both material and symmetry aspects, are unveiled and connected to fundamental conservation laws and nonsymmorphic space group. Our study paves the way toward the synergy between three-dimensional mechanical metamaterials and topological wave dynamics.

cond-mat.mes-hall↗

arXiv2017

Type-II Dirac Photons

The Dirac equation for relativistic electron waves is the parent model for Weyl and Majorana fermions as well as topological insulators. Simulation of Dirac physics in three-dimensional photonic crystals, though fundamentally important for topological phenomena at optical frequencies, encounters the challenge of synthesis of both Kramers double degeneracy and parity inversion. Here we show how type-II Dirac points---exotic Dirac relativistic waves yet to be discovered---are robustly realized through the nonsymmorphic screw symmetry. The emergent type-II Dirac points carry nontrivial topology and are the mother states of type-II Weyl points. The proposed all-dielectric architecture enables robust cavity states at photonic-crystal---air interfaces and anomalous refraction, with very low energy dissipation.

physics.optics↗

arXiv2017

Quantum many-body simulation using monolayer exciton-polaritons in coupled-cavities

Quantum simulation is a promising approach to understand complex strongly correlated many-body systems using relatively simple and tractable systems. Photon-based quantum simulators have great advantages due to the possibility of direct measurements of multi-particle correlations and ease of simulating non-equilibrium physics. However, interparticle interaction in existing photonic systems is often too weak limiting the potential of quantum simulation. Here we propose an approach to enhance the interparticle interaction using exciton-polaritons in MoS$_2$ monolayer quantum-dots embedded in 2D photonic crystal microcavities. Realistic calculation yields optimal repulsive interaction in the range of $1$-$10$~meV --- more than an order of magnitude greater than the state-of-art value. Such strong repulsive interaction is found to emerge neither in the photon-blockade regime for small quantum dot nor in the polariton-blockade regime for large quantum dot, but in the crossover between the two regimes with a moderate quantum-dot radius around 20~nm. The optimal repulsive interaction is found to be largest in MoS$_2$ among commonly used optoelectronic materials. Quantum simulation of strongly correlated many-body systems in a finite chain of coupled cavities and its experimental signature are studied via exact diagonalization of the many-body Hamiltonian. A method to simulate 1D superlattices for interacting exciton-polariton gases in serially coupled cavities is also proposed. Realistic considerations on experimental realizations reveal advantages of transition metal dichalcogenide monolayer quantum-dots over conventional semiconductor quantum-emitters.

cond-mat.mes-hall↗