Universal probes of two-dimensional topological insulators: Dislocation and pi-flux

TL;DR

This paper demonstrates that pi-flux and dislocations serve as topological probes in 2D topological insulators, revealing zero-energy modes that help classify different phases and are robust against disorder.

Contribution

It analytically and numerically shows how pi-flux and dislocations reveal zero modes in 2D topological insulators, aiding in their classification.

Findings

Pi-flux hosts Kramers pairs of zero modes in topological phases.

Dislocations act as pi-flux only in the M phase, binding zero modes.

Zero modes are robust to disorder and Rashba coupling.

Abstract

We show that the pi-flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that pi-flux hosts a Kramers pair of zero modes in the topological Gamma (Berry phase skyrmion at the zero momentum) and M (Berry phase skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a pi-flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.