Topology in time-reversal symmetric crystals

Abstract

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are used to label distinct types of topological insulators. But it is not generally known how many or which invariants can exist in any given crystalline material. Using a new and efficient counting algorithm, we study the topological invariants that arise in time-reversal symmetric crystals. This results in a unified picture that explains the relations between all known topological invariants in these systems. It also predicts new topological phases and one entirely new topological invariant. We present explicitly the classification of all two-dimensional crystalline fermionic materials, and give a straightforward procedure for finding the analogous result in any three-dimensional structure. Our study represents a single, intuitive physical picture applicable to all topological invariants in real materials, with crystal symmetries.

13 pages, 4 figures, revised version

References in corpus (10)

• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• The space group classification of topological band insulators
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Fragile Topology and Wannier Obstructions
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect

Cited by in corpus (10)

• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• The hybrid-order topology of weak topological insulators
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• The topological invariants of rotationally symmetric crystals
• Homotopy invariant in time-reversal and twofold rotation symmetric systems
• Visualizing topological transport