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arXiv:2512.21179

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

Jiaxin Pan, Longwen Zhou

cond-mat.mes-hallquant-phSubmitted Dec 24, 2025• Announced Dec 25, 2025• Revised Dec 30, 2025 (v2)

v1 · Dec 24, 2025 v2 · Dec 30, 2025 v3 · May 14, 2026

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.

Journal reference: Phys. Rev. B 113, 195405 (2026)
DOI: 10.1103/kx2n-d3qs
Comments: 16 pages, 7 figures

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