The space group classification of topological band insulators

Abstract

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.

Accepted in Nature Physics

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• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Exploration and prediction of topological electronic materials based on first-principles calculations
• Quantum superconducting criticality in graphene and topological insulators
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• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Spin-polarized (001) surface states of the topological crystalline insulator Pb_{0.73}Sn_{0.27}Se
• Topological states in multi-orbital HgTe honeycomb lattices
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• CPT theorem and classification of topological insulators and superconductors
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Spin and valley transports in junctions of Dirac fermions
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Extended topological group structure due to average reflection symmetry
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• High-Chern-number bands and tunable Dirac cones in $\beta$-graphyne
• Characterizing the weak topological properties: Berry phase point of view
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator