Browse
Submit Data
Databases
API
Help

Dataset Information

21 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Topological states from topological crystals.

ABSTRACT: We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.

SUBMITTER: Song Z

PROVIDER: S-EPMC6920025 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Topological states from topological crystals.

Song Zhida Z Huang Sheng-Jie SJ Qi Yang Y Fang Chen C Hermele Michael M

Science advances 20191218 12

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry grou ...[more]

PMID: 31897424

Similar Datasets

Higher-Order Topological States in Surface-Wave Photonic Crystals.

Project description:Photonic topological states have revolutionized the understanding of the propagation and scattering of light. The recent discovery of higher-order photonic topological insulators opens an emergent horizon for 0D topological corner states. However, the previous realizations of higher-order topological insulators in electromagnetic-wave systems suffer from either a limited operational frequency range due to the lumped components involved or a bulky structure with a large footprint, which are unfavorable for achieving compact photonic devices. To overcome these limitations, a planar surface-wave photonic crystal realization of 2D higher-order topological insulators is hereby demonstrated experimentally. The surface-wave photonic crystals exhibit a very large bulk bandgap (a bandwidth of 28%) due to multiple Bragg scatterings and host 1D gapped edge states described by massive Dirac equations. The topology of those higher-dimensional photonic bands leads to the emergence of in-gap 0D corner states, which provide a route toward robust cavity modes for scalable compact photonic devices.

| S-EPMC7080542 | biostudies-literature

Three-dimensional topological acoustic crystals with pseudospin-valley coupled saddle surface states.

Project description:Topological valley states at the domain wall between two artificial crystals with opposite valley Chern numbers offer a feasible way to realize robust wave transport since only broken spatial symmetry is required. In addition to the valley, spin and crystal dimension are two other important degrees of freedom, particularly in realizing spin-related topological phenomena. Here we experimentally demonstrate that it is possible to construct two-dimensional acoustic topological pseudospin-valley coupled saddle surface states, designed from glide symmetry in a three-dimensional system. By taking advantage of such two-dimensional surface states, a full set of acoustic pseudospins can be realized, exhibiting pseudospin-valley dependent transport. Furthermore, due to the hyperbolic character of the dispersion of saddle surface states, multi-directional anisotropic controllable robust sound transport with little backscattering is observed. Our findings may open research frontiers for acoustic pseudospins and provide a satisfactory platform for exploring unique acoustic topological properties in three-dimensional structures.

| S-EPMC6212403 | biostudies-literature

Direct observation of valley-polarized topological edge states in designer surface plasmon crystals.

Project description:The extensive research of two-dimensional layered materials has revealed that valleys, as energy extrema in momentum space, could offer a new degree of freedom for carrying information. Based on this concept, researchers have predicted valley-Hall topological insulators that could support valley-polarized edge states at non-trivial domain walls. Recently, several kinds of photonic and sonic crystals have been proposed as classical counterparts of valley-Hall topological insulators. However, direct experimental observation of valley-polarized edge states in photonic crystals has remained difficult until now. Here, we demonstrate a designer surface plasmon crystal comprising metallic patterns deposited on a dielectric substrate, which can become a valley-Hall photonic topological insulator by exploiting the mirror-symmetry-breaking mechanism. Topological edge states with valley-dependent transport are directly visualized in the microwave regime. The observed edge states are confirmed to be fully valley-polarized through spatial Fourier transforms. Topological protection of the edge states at sharp corners is also experimentally demonstrated.

| S-EPMC5670222 | biostudies-literature

Quadrupole topological photonic crystals.

Project description:Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell's equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.

| S-EPMC7305167 | biostudies-literature

Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing.

Project description:Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical, exhibiting unidirectional propagation that is topologically protected against back scattering. We directly observe the topological states of a photonic analog of electronic materials exhibiting the quantum spin Hall effect, living at the interface between two silicon photonic crystals with different topological order. Through the far-field radiation that is inherent to the states' existence, we characterize their properties, including linear dispersion and low loss. We find that the edge state pseudospin is encoded in unique circular far-field polarization and linked to unidirectional propagation, thus revealing a signature of the underlying photonic spin-orbit coupling. We use this connection to selectively excite different edge states with polarized light and directly visualize their routing along sharp chiral waveguide junctions.

| S-EPMC7075695 | biostudies-literature

Controlling Topological States in Topological/Normal Insulator Heterostructures.

Project description:We have performed a systematic investigation of the nature of the nontrivial interface states in topological/normal insulator (TI/NI) heterostructures. On the basis of first principles and a recently developed scheme to construct ab initio effective Hamiltonian matrices from density functional theory calculations, we studied systems of realistic sizes with high accuracy and control over the relevant parameters such as TI and NI band alignment, NI gap, and spin-orbit coupling strength. Our results for IV-VI compounds show the interface gap tunability by appropriately controlling the NI thickness, which can be explored for device design. Also, we verified the preservation of an in-plane spin texture in the interface-gaped topological states.

| S-EPMC6643377 | biostudies-literature

Electrically-tunable positioning of topological defects in liquid crystals.

Project description:Topological defects are a consequence of broken symmetry in ordered systems and are important for understanding a wide variety of phenomena in physics. In liquid crystals (LCs), defects exist as points of discontinuous order in the vector field that describes the average orientation of the molecules in space and are crucial for explaining the fundamental behaviour and properties of these mesophases. Recently, LC defects have also been explored from the perspective of technological applications including self-assembly of nanomaterials, optical-vortex generation and in tunable plasmonic metamaterials. Here, we demonstrate the fabrication and stabilisation of electrically-tunable defects in an LC device using two-photon polymerisation and explore the dynamic behaviour of defects when confined by polymer structures laser-written in topologically discontinuous states. We anticipate that our defect fabrication technique will enable the realisation of tunable, 3D, reconfigurable LC templates towards nanoparticle self-assembly, tunable metamaterials and next-generation spatial light modulators for light-shaping.

| S-EPMC7200663 | biostudies-literature

Mesoscale martensitic transformation in single crystals of topological defects.

Project description:Liquid-crystal blue phases (BPs) are highly ordered at two levels. Molecules exhibit orientational order at nanometer length scales, while chirality leads to ordered arrays of double-twisted cylinders over micrometer scales. Past studies of polycrystalline BPs were challenged by the existence of grain boundaries between randomly oriented crystalline nanodomains. Here, the nucleation of BPs is controlled with precision by relying on chemically nanopatterned surfaces, leading to macroscopic single-crystal BP specimens where the dynamics of mesocrystal formation can be directly observed. Theory and experiments show that transitions between two BPs having a different network structure proceed through local reorganization of the crystalline array, without diffusion of the double-twisted cylinders. In solid crystals, martensitic transformations between crystal structures involve the concerted motion of a few atoms, without diffusion. The transformation between BPs, where crystal features arise in the submicron regime, is found to be martensitic in nature when one considers the collective behavior of the double-twist cylinders. Single-crystal BPs are shown to offer fertile grounds for the study of directed crystal nucleation and the controlled growth of soft matter.

| S-EPMC5617308 | biostudies-literature

Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals.

Project description:We present an active, purely mechanical stress wave isolator that consists of short cylindrical particles arranged in a helical architecture. This phononic structure allows us to change inter-particle stiffness dynamically by controlling the contact angles of the cylinders. We use torsional travelling waves to control the contact angles, thereby imposing a desired spatio-temporal stiffness variation to the phononic crystal along the longitudinal direction. Such torsional excitation is a form of parametric pumping in the system, which results in the breakage of the time-reversal symmetry. We report that, in quasi-static sense, the system shows topologically non-trivial band-gaps. However, in a dynamic regime where the pumping effect is significant, these band-gaps become asymmetric with respect to the frequency and wavenumber domains in the dispersion relationship. By using numerical simulations, we show that such asymmetry has a direct correspondence to the topological invariant, i.e., Chern number, of the system. We propose that this asymmetry, accompanied by selective inter-band transition, can be utilized for directional isolation of the stress wave propagating along the phononic crystal.

| S-EPMC4967924 | biostudies-literature

Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices.

Project description:The scattering of Dirac electrons by topological defects could be one of the most relevant sources of resistance in graphene and at the boundary surfaces of a three-dimensional topological insulator (3D TI). In the long wavelength, continuous limit of the Dirac equation, the topological defect can be described as a distortion of the metric in curved space, which can be accounted for by a rotation of the Gamma matrices and by a spin connection inherited with the curvature. These features modify the scattering properties of the carriers. We discuss the self-energy of defect formation with this approach and the electron cross-section for intra-valley scattering at an edge dislocation in graphene, including corrections coming from the local stress. The cross-section contribution to the resistivity, ρ, is derived within the Boltzmann theory of transport. On the same lines, we discuss the scattering of a screw dislocation in a two-band 3D TI, like Bi1-xSbx, and we present the analytical simplified form of the wavefunction for gapless helical states bound at the defect. When a 3D TI is sandwiched between two even-parity superconductors, Dirac boundary states acquire superconductive correlations by proximity. In the presence of a magnetic vortex piercing the heterostructure, two Majorana states are localized at the two interfaces and bound to the vortex core. They have a half integer total angular momentum each, to match with the unitary orbital angular momentum of the vortex charge.

| S-EPMC5453268 | biostudies-other

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data