Coupled-wire construction of non-Abelian higher-order topological phases

TL;DR

This paper introduces a coupled-wire approach to construct non-Abelian higher-order topological phases, revealing new boundary states and phase transitions that extend topological classifications beyond Abelian invariants.

Contribution

It proposes a novel coupled-wire scheme for non-Abelian HOTPs, analyzing a minimal model with hybridized corner modes protected by combined symmetries.

Findings

Supports corner modes protected by non-Abelian quaternion and Abelian winding invariants.

Shows emergence of weak topological edge states from non-Abelian origins.

Demonstrates both non-Abelian and Abelian phase transitions in the system.

Abstract

Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme of constructing non-Abelian HOTPs and analyze a non-Abelian second-order topological insulator as its minimal model. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time-reversal plus sublattice symmetries and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origins arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits both non-Abelian and Abelian topological phase transitions, providing a unified platform that bridges these two distinct topological classes. Our work extends the understanding of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum systems, such as photonic or acoustic metamaterials.