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.

arXiv commentFinal version, 27 pages, 7 figures

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• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Electric polarization in a Chern insulator
• One-Dimensional Edge Transport in Few-Layer WTe${}_2$
• Symmetry-Enforced Weyl Phonons
• Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
• Discovering new two-dimensional topological insulators from computational screening
• Optical Signatures of Dirac Nodal-lines in NbAs${}_2$
• Resolving the Topological Classification of Bismuth with Topological Defects
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Multiple Flat Bands and Topological Hofstadter Butterfly in Twisted Bilayer Graphene Close to the Second Magic Angle
• The Dirac-Weyl semimetal: Coexistence of Dirac and Weyl fermions in polar hexagonal $ABC$ crystals
• Multifold nodal points in magnetic materials
• The Axion Insulator as a Pump of Fragile Topology
• Bulk and surface electronic structure of the dual-topology semimetal Pt2HgSe3
• Symmetry indicators of band topology
• Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings
• Partial lattice defects in higher order topological insulators
• Chiral fermion reversal in chiral crystals
• Fractionalization in a square-lattice model with time-reversal symmetry
• Classification of topological crystalline insulators based on representation theory
• Type-II Dirac semimetals in the YPd${}_2$Sn class
• Network Models of Quantum Percolation and Their Field-Theory Representations
• Experimental observation of bulk nodal lines and electronic surface states in ZrB${}_2$
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Application of topological quantum chemistry in electrides
• Six-fold Excitations in Electrides
• Half quantum spin Hall effect on the surface of weak topological insulators
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Density wave instabilities and surface state evolution in interacting Weyl semimetals
• Observation of multiple types of topological fermions in PdBiSe
• Dual topology in Jacutingaite Pt${}_2$HgSe${}_3$
• Ultraquantum magnetoresistance in single-crystalline $\beta$-Ag${}_2$Se
• Ultraquantum magnetoresistance in Kramers Weyl semimetal candidate $\beta$-Ag2Se
• Quantum Spin Hall Effect in Ta${}_2$M${}_3$Te${}_5$ (M = Pd, Ni)
• Pfaffian formalism for higher-order topological insulators
• $\beta$-CuI: a Dirac semimetal without surface Fermi arcs
• Direct observation of six-fold exotic fermions in topological semimetal PdSb${}_2$
• Canonical magnetic insulators with isotropic magnetoelectric coupling
• Two-dimensional topological materials discovery by symmetry-indicator method
• Topological Nodal Line Electrides: Realization of Ideal Nodal Line State Nearly Immune from Spin-Orbit Coupling
• Pairing Obstructions in Topological Superconductors
• Emergent dual topology in the three-dimensional Kane-Mele Pt${}_2$HgSe${}_3$
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Critical Behavior and Universal Signature of an Axion Insulator State
• Axion coupling in the hybrid Wannier representation
• Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks
• Edge superconductivity in Multilayer WTe2 Josephson junction
• Delocalization Transition of Disordered Axion Insulator
• Higher-order topological insulators in antiperovskites
• Deformation and Stability of Surface States in Dirac semimetals
• Imaging electronic states on topological semimetals using scanning tunneling microscopy
• Strongly correlated double Dirac fermions
• Topology invisible to eigenvalues in obstructed atomic insulators
• Fermi surface, possible unconventional fermions, and unusually robust resistive critical fields in the chiral-structured superconductor AuBe
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Holographic Maps of Quasiparticle Interference
• A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSb
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Weyl Semimetals with $S_4$ symmetry
• Anomalous localization at the boundary of an interacting topological insulator
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Threes Company
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Topological electronic properties of silicon
• Ultralong carrier lifetime of topological edge states in a-Bi4Br4
• Observation of the Topologically Originated Edge States in large-gap Quasi-One-Dimensional a-Bi${}_4$Br${}_4$

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• 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
• Machine learning spectral indicators of topology
• 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
• Layer group classification of two-dimensional materials
• Obstructed insulators and flat bands in topological phase-change 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
• Effective action approach to the filling anomaly in crystalline topological matter
• Large anomalous Hall, Nernst effect and topological phases in the 3d-4d/5d based oxide double perovskites
• Big bang as a topological quantum phase transition
• Observation of nonlinear topological corner states originating from different spectral charges
• Topological Phase Transition in Quasi-One-Dimensional Bismuth Iodide Bi4I4
• Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping
• 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
• 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
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Higher-order topology in twisted multilayer systems: a review
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• STM observation of the hinge-states of bismuth nanocrystals
• 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
• Topological Spectral Bands with Frieze Groups
• Quadratic solitons in higher-order topological insulators
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Polariton Topological Insulators with Disclinations
• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Topological insulators and geometry of vector bundles
• Non-equilibrium States and Interactions in the Topological Insulator and Topological Crystalline Insulator Phases of NaCd4As3
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Localized interfacial Phonon Modes at the Electronic Axion Domain Wall
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Coupled-wire construction of non-Abelian higher-order topological phases
• Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Van Roosbroeck's equations with topological terms: the case of Weyl semimetals
• Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
• Weak ${\mathbb{Z}}_2$ Supertopology
• Investigating the intrinsic anomalous Hall effect in MnPt3 topological semimetal
• First-principles studies of fermiology in topological phases of bulk ZrTe${}_5$
• Entanglement entropy as a probe of topological phase transitions
• Dynamically tuneable helicity in twisted electromagnetic resonators