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

Understand

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.