Four-band non-Abelian topological insulator and its experimental realization

TL;DR

This paper introduces a comprehensive study and experimental realization of four-band non-Abelian topological insulators, revealing new topological charges and edge states, and highlighting differences from Abelian systems.

Contribution

It provides the first detailed theoretical and experimental analysis of four-band non-Abelian topological insulators, including new classes of topological charges and edge states.

Findings

Identification of new non-Abelian topological charges

Experimental realization of a four-band system with non-Abelian topology

Analysis of edge state distributions and bulk topology evolution

Abstract

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.