Stable boundary modes for fragile topology from spontaneous PT-symmetry breaking

TL;DR

This paper demonstrates that non-Hermitian couplings in PT-symmetric systems can induce stable in-gap topological edge modes, transforming fragile topology into robust phenomena through spontaneous PT-symmetry breaking.

Contribution

It introduces a mechanism for stabilizing topological edge modes in fragile topological systems via non-Hermitian perturbations that break PT symmetry spontaneously.

Findings

Robust in-gap edge modes can be induced by non-Hermitian couplings.

Topological edge modes traverse the imaginary spectral gap.

Net number of in-gap modes is protected by an anomaly cancellation mechanism.

Abstract

Two-dimensional topological insulators protected by nonlocal symmetries or with fragile topology usually do not admit robust in-gap edge modes due to the incompatibility between the symmetry and the boundary. Here, we show that in a parity-time (PT) symmetric system robust in-gap topological edge modes can be stably induced by non-Hermitian couplings that spontaneously break the PT symmetry of the eigenstates. The topological edge modes traverse the imaginary spectral gap between a pair of fragile topological bands, which is opened by the presence of the non-Hermitian perturbation. We demonstrate that the net number of resulting in-gap modes is protected by an operator version of anomaly cancellation that extends beyond the Hermitian limit. The results imply that loss and gain can in principle drive fragile topological phenomena to stable topological phenomena.