Edge and corner states in 2D non-Abelian topological insulators from an eigenvector frame rotation perspective

TL;DR

This paper introduces a new framework for understanding 2D non-Abelian topological insulators, explaining edge and corner states through non-Abelian band topology, and proposes off-diagonal Berry phase as a predictive tool.

Contribution

It establishes constraints on 2D Zak phase and polarization, and links corner states to boundary modes of 1D edge states within a non-Abelian topological context.

Findings

Corner states explained as boundary modes of 1D edge states

Off-diagonal Berry phase aids in predicting edge states

Framework applicable to 3D systems

Abstract

We propose the concept of 2D non-Abelian topological insulator which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the 1D edge states arising from the multi-band non-Abelian topology of the system. We also propose the use of off-diagonal Berry phase as complementary information to assist the prediction of edge states in non-Abelian topological insulators. Our work provides an alternative approach to study edge and corner modes and this idea can be extended to 3D systems.