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

• Published in: Nature communications Vol. 12; no. 1; p. 6471
• Main Authors: Jiang, Tianshu, Guo, Qinghua, Zhang, Ruo-Yang, Zhang, Zhao-Qing, Yang, Biao, Chan, C. T.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 09-11-2021; Nature Publishing Group; Nature Portfolio
• Subjects: 639/624/399/1022; 639/766/119/2792/4128; Algebra; Eigenvalues; Energy gap; Humanities and Social Sciences; multidisciplinary; Phase transitions; Quaternions; Science; Science (multidisciplinary); Topological insulators; Topology; Toruses
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-021-26763-1

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q
8
. 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.
Non-Abelian topological insulators receive increasing attention due to entangled bulk bandgaps different from Abelian counterparts. Here, the authors realize two new classes of topological charges characterizing of a four-band non-Abelian topological insulator.