Spontaneous breakdown of topological protection in two dimensions

TL;DR

This paper demonstrates that realistic smooth edge potentials in two-dimensional topological insulators can cause edge reconstruction and spontaneous time-reversal symmetry breaking, challenging the robustness of topological protection in practical systems.

Contribution

It reveals that realistic edge conditions can lead to spontaneous TRS breaking and edge reconstruction, undermining the assumed perfect conductance in topological insulators.

Findings

Edge reconstruction occurs with smooth edge potentials.

Spontaneous TRS breaking can lead to finite Hall resistance.

Topological protection is fragile in realistic conditions.

Abstract

Due to time-reversal symmetry (TRS), two dimensional topological insulators support counter-propagating helical edge modes. Here we show that, unlike the infinitely sharp edge potential utilized in traditional calculations, an experimentally more realistic smooth edge potential gives rise to edge reconstruction and, consequently, spontaneous TRS breaking. Such edge reconstruction may lead to breaking of the expected perfect conductance quantization, to a finite Hall resistance at zero magnetic field, and to a likely spin current. This calculation underpins the fragility of the topological protection in realistic systems, which is of crucial importance in proposed applications.