Topological Materials Discovery from Crystal Symmetry

Abstract

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs), and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures - including the theory of Topological Quantum Chemistry (TQC) - researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of all of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85% of the known stoichiometric materials host energetically isolated topological bands, and that just under $2/3$ of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.

Final version, 27 pages, 7 figures

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Cited by in corpus (57)

• Topological acoustics
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• Amorphous topological matter: theory and experiment
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Classification of Dirac points with higher-order Fermi arcs
• The Wannier Function Software Ecosystem for Materials Simulations
• Topology invisible to eigenvalues in obstructed atomic insulators
• Obstructed insulators and flat bands in topological phase-change materials
• Layer group classification of two-dimensional materials
• MSGCorep: A package for corepresentations of magnetic space groups
• Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Bimerons create bimerons: proliferation and aggregation induced by currents and magnetic fields
• Spin-momentum locking from topological quantum chemistry: applications to multifold fermions
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Large anomalous Hall, Nernst effect and topological phases in the 3d-4d/5d based oxide double perovskites
• Effective action approach to the filling anomaly in crystalline topological matter
• Big bang as a topological quantum phase transition
• Topological Phase Transition in Quasi-One-Dimensional Bismuth Iodide Bi4I4
• Observation of nonlinear topological corner states originating from different spectral charges
• Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model
• Spin-polarization of topological crystalline and normal insulator Pb${}_{1-x}$Sn${}_x$Se (111) epilayers probed by photoelectron spectroscopy
• Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping
• Revealing the topological phase diagram of ZrTe${}_5$ using the complex strain fields of microbubbles
• Fully-gapped superconductivity and topological aspects of the noncentrosymmetric TaReSi superconductor
• STM observation of the hinge-states of bismuth nanocrystals
• Higher-order topology in twisted multilayer systems: a review
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• Two-dimensional orbital-obstructed insulators with higher-order band topology
• Chiral anomaly-induced nonlinear Hall effect in spin-orbit coupled noncentrosymmetric metals
• Disorder and diffuse scattering in single-chirality (TaSe${}_4$)${}_2$I crystals
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Multiband superconductivity in the topological Kramers nodal-line semimetals
• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Polariton Topological Insulators with Disclinations
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Quadratic solitons in higher-order topological insulators
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Non-equilibrium States and Interactions in the Topological Insulator and Topological Crystalline Insulator Phases of NaCd4As3
• Topological Spectral Bands with Frieze Groups
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Localized interfacial Phonon Modes at the Electronic Axion Domain Wall
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Weak ${\mathbb{Z}}_2$ Supertopology
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Entanglement entropy as a probe of topological phase transitions
• Dynamically tuneable helicity in twisted electromagnetic resonators
• Coupled-wire construction of non-Abelian higher-order topological phases
• Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
• Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
• Van Roosbroeck's equations with topological terms: the case of Weyl semimetals
• Investigating the intrinsic anomalous Hall effect in MnPt3 topological semimetal
• First-principles studies of fermiology in topological phases of bulk ZrTe${}_5$