Topological Wannier cycles for the bulk and edges

TL;DR

This paper introduces a robust method using local artificial gauge flux to detect higher-order topological insulators through spectral flows, even when chiral symmetry is broken, extending the concept of Wannier cycles to various symmetries.

Contribution

It develops a new approach employing artificial gauge flux to probe topological phases, extending Wannier cycles to systems with C2 and C3 symmetries, and reveals their effectiveness in detecting bulk and edge topological features.

Findings

Artificial gauge flux induces cyclic spectral flows in topological insulators.

Wannier cycles can be extended to systems with C2 and C3 symmetries.

Spectral flows reveal topological properties even with broken chiral symmetry.

Abstract

Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral topological characteristics are extended from edge states to corner states. However, the chiral symmetry protecting the corner states is often broken in genuine materials, leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant. Here, we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators which is effective even when the chiral symmetry is broken. The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps. These spectral flows are associated with the local modes bound to the artificial gauge flux. This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them. We extend topological Wannier cycles to systems with C2 and C3 symmetries and show that they can probe both the bulk and the edge Wannier centers, yielding rich topological phenomena.