Real-space Obstruction in Quantum Spin Hall Insulators

TL;DR

This paper extends the concept of topological obstructions from atomic insulators to quantum spin Hall insulators, identifying real-space obstructions and their experimental signatures in a large-gap material.

Contribution

It introduces a new classification of quantum spin Hall insulators based on real-space obstructions and demonstrates their experimental detection.

Findings

Identification of a graphene-like system with real-space obstruction

Development of a low-energy model with spin-orbit coupling and symmetry breaking

Experimental measurement of obstruction in a large-gap quantum spin Hall material

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.