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

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. 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.

Automated summary

The study presents two new classes of topological charges for four-band non-Abelian topological insulators, revealing significant differences in non-Abelian topological classification for even-band systems. The research illustrates the evolution of bulk topology and edge state distributions in a four-band PT symmetric system, paving the way for further exploration of even-band systems.