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

References in corpus (14)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Helical Metal Inside a Topological Band Insulator
• Universal phase diagrams for the quantum spin Hall systems
• Observation of Topological Crystalline Insulator phase in the lead tin chalcogenide Pb1-xSnxTe material class

Cited by in corpus (7)

• A classification of symmetry enriched topological phases with exactly solvable models
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
• Quantum superconducting criticality in graphene and topological insulators
• 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
• Extended topological group structure due to average reflection symmetry