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 entangled bulk bandgaps and support nontrivial edge states that manifest the non-Abelian topological features. Furthermore, a system with an even or odd number of bands will exhibit a significant difference in non-Abelian topological classification. To date, there has been scant research investigating even-band non-Abelian topological insulators. Here, we both theoretically explore and experimentally realize 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 in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. We show the evolution of the 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 towards other even-band systems.
Highlights
Very recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8
If we focus on a single bandgap, topological physical systems[1–6] are usually classified by Abelian groups, with the prime example being the tenfold classification[7,8] of Hermitian topological insulators and superconductors
A simple argument for this is that the even-dimensional special orthogonal groups, i.e., SOð2NÞ, with N indicating a positive integer, contain inversion symmetry, i.e., ÀI2N
Summary
Very recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8. There has been scant research investigating even-band non-Abelian topological insulators. We both theoretically explore and experimentally realize 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 in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. For systems with an even number of bands, several new classes of non-Abelian topological charges deserve special attention. A simple argument for this is that the even-dimensional special orthogonal groups, i.e., SOð2NÞ, with N indicating a positive integer, contain inversion symmetry, i.e., ÀI2N (the negative 2N 2N identity matrix)
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