arXiv subjects

Zhi-Kang Lin

Publications and source records attributed to Zhi-Kang Lin.

32 records · Page 2Linked to original sources

arXiv2021

Dirac cones and higher-order topology in quasi-continuous media

We consider the Dirac cones and higher-order topological phases in quasi-continuous media of classical waves (e.g., photonic and sonic crystals). Using sonic crystals as prototype examples, we revisit some of the known systems in the study of topological acoustics. We show the emergence of various Dirac cones and higher-order topological band gaps in the same motherboard by tuning the geometry of the system. We provide a pedagogical review of the underlying physics and methodology via the bulk-edge-corner correspondence, symmetry-based indicators, Wannier representations, filling anomaly, and fractional corner charges. In particular, the theory of the Dirac cones and the higher-order topology are put in the same framework. These examples and the underlying physics principles can be inspiring and useful in the future study of higher-order topological metamaterials.

cond-mat.mtrl-sci↗

arXiv2021

Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles

Gauge fields are at the heart of the fundamental science of our universe and various materials. For instance, Laughlin's gedanken experiment of gauge flux insertion played a major role in understanding the quantum Hall effects. Gauge flux insertion into a single unit-cell, though crucial for detecting exotic quantum phases and for the ultimate control of quantum dynamics and classical waves, however, has not yet been achieved in laboratory. Here, we report on the experimental realization of gauge flux insertion into a single plaquette in a lattice system with the gauge phase ranging from 0 to 2pi which is realized through a novel approach based on three consecutive procedures: the dimension extension, creating an engineered dislocation and the dimensional reduction. Furthermore, we discover that the single-plaquette gauge flux insertion leads to a new phenomenon termed as the topological Wannier cycles, i.e., the cyclic spectral flows across multiple band gaps which are manifested as the topological boundary states (TBSs) on the plaquette. Such topological Wannier cycles emerge only if the Wannier centers are enclosed by the flux-carrying plaquette. Exploiting acoustic metamaterials and versatile pump-probe measurements, we observe the topological Wannier cycles by detecting the TBSs in various ways and confirm the single-plaquette gauge flux insertion by measuring the gauge phase accumulation on the plaquette. Our work unveils an unprecedented regime for lattice gauge systems and a fundamental topological response which could empower future studies on artificial gauge fields and topological materials.

cond-mat.mtrl-sci↗

arXiv2021

Observation of Higher-Order Topological States in Acoustic Twisted Moiré Superlattice

Twisted moiré superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moiré twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topological edge and corner states, which can be understood via the Wannier centers of the acoustic Bloch bands below the band gap. We confirm experimentally the higher-order band topology by characterizing the edge and corner states using acoustic pump-probe measurements. With complementary theory and experiments, our study opens a pathway toward band topology in TMSs.

cond-mat.mtrl-sci↗

arXiv2021

Observation of non-Abelian topological semimetals and their phase transitions

Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have almost exclusively been restricted to single-gap band topology because of the Fermi-Dirac filling effect. Here, we theoretically analyze and experimentally confirm a novel class of multi-gap topological phases, which we will refer to as non-Abelian topological semimetals, on kagome geometries. These unprecedented forms of matter depend on the notion of Euler class and frame charges which arise due to non-Abelian charge conversion processes when band nodes of different gaps are braided along each other in momentum space. We identify such exotic phenomena in acoustic metamaterials and uncover a rich topological phase diagram induced by the creation, braiding and recombination of band nodes. Using pump-probe measurements, we verify the non-Abelian charge conversion processes where topological charges of nodes are transferred from one gap to another. Moreover, in such processes, we discover symmetry-enforced intermediate phases featuring triply-degenerate band nodes with unique dispersions that are directly linked to the multi-gap topological invariants. Furthermore, we confirm that edge states can faithfully characterize the multi-gap topological phase diagram. Our study unveils a new regime of topological phases where multi-gap topology and non-Abelian charges of band nodes play a crucial role in understanding semimetals with inter-connected multiple bands.

cond-mat.mes-hall↗

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

Experimental discovery of bulk-disclination correspondence

Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however, becomes inadequate in discerning various topological crystalline phases [7-17], leading to great challenges in the experimental classification of the large family of topological crystalline materials [4-6]. Theories predict that disclinations, ubiquitous crystallographic defects, provide an effective probe of crystalline topology beyond edges [18-21], which, however, has not yet been confirmed in experiments. Here, we report the experimental discovery of the bulk-disclination correspondence which is manifested as the fractional spectral charge and robust bound states at the disclinations. The fractional disclination charge originates from the symmetry-protected bulk charge patterns---a fundamental property of many topological crystalline insulators (TCIs). Meanwhile, the robust bound states at disclinations emerge as a secondary, but directly observable property of TCIs. Using reconfigurable photonic crystals as photonic TCIs with higher-order topology, we observe those hallmark features via pump-probe and near-field detection measurements. Both the fractional charge and the localized states are demonstrated to emerge at the disclination in the TCI phase but vanish in the trivial phase. The experimental discovery of bulk-disclination correspondence unveils a novel fundamental phenomenon and a new paradigm for exploring topological materials.

cond-mat.mtrl-sci↗

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

Twisted quadrupole topological photonic crystals

Topological manipulation of waves is at the heart of the cutting-edge metamaterial researches. Quadrupole topological insulators were recently discovered in two-dimensional (2D) flux-threading lattices which exhibit higher-order topological wave trapping at both the edges and corners. Photonic crystals (PhCs), lying at the boundary between continuous media and discrete lattices, however, are incompatible with the present quadrupole topological theory. Here, we unveil quadrupole topological PhCs triggered by a twisting degree-of-freedom. Using a topologically trivial PhC as the motherboard, we show that twisting induces quadrupole topological PhCs without flux-threading. The twisting-induced crystalline symmetry enriches the Wannier polarizations and lead to the anomalous quadrupole topology. Versatile edge and corner phenomena are observed by controlling the twisting angles in a lateral heterostructure of 2D PhCs. Our study paves the way toward topological twist-photonics as well as the quadrupole topology in the quasi-continuum regime for phonons and polaritons.

cond-mat.mes-hall↗

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

Plasmon-polaritonic quadrupole topological insulators

Quadrupole topological insulator is a symmetry-protected higher-order topological phase with intriguing topology of Wannier bands, which, however, has not yet been realized in plasmonic metamaterials. Here, we propose a lattice of plasmon-polaritonic nanocavities which can realize quadrupole topological insulators by exploiting the geometry-dependent sign-reversal of the couplings between the daisy-like nanocavities. The designed system exhibits various topological and trivial phases as characterized by the nested Wannier bands and the topological quadrupole moment which can be controlled by the distances between the nanocavities. Our study opens a pathway toward plasmonic topological metamaterials with quadrupole topology.

physics.optics↗

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↗