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

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.

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

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.

A new class of killing invariant surfaces in 𝕊3

The aim of this note is to characterize Clifford tori as the only Killing invariant surfaces, under an additional hypothesis. Moreover, we build a family of Killing invariant minimal surfaces in [Formula: see text], that does not contain Clifford tori as well as we present examples of Killing invariant surfaces whose mean curvature is not identically zero.