Real-space Obstruction in Quantum Spin Hall Insulators

Abstract

The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied via symmetry analysis as well as with density functional theory. The low-energy model comprises a local spin-orbit coupling and a non-local symmetry breaking potential, which turn out to be the essential ingredients for an obstructed quantum spin Hall insulator. An experimental fingerprint of the obstruction is then measured in a large-gap triangular quantum spin Hall material.

9 pages, 6 figures and 1 table. Supplementary material: 5 pages, 4 figures and 2 tables

References in corpus (14)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Spin-orbit gap of graphene: First-principles calculations
• Reflection symmetric second-order topological insulators and superconductors
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Computing topological invariants without inversion symmetry
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• On the $Z_2$ classification of Quantum Spin Hall Models
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Design and realization of topological Dirac fermions on a triangular lattice