Non-Hermitian non-Abelian topological insulators with $PT$ symmetry

Abstract

We study a non-Hermitian non-Abelian topological insulator preserving $PT$ symmetry, where the non-Hermitian term represents nonreciprocal hoppings. As it increases, a spontaneous $PT$ symmetry breaking transition occurs in the perfect-flat band model from a real-line-gap topological insulator into an imaginary-line-gap topological insulator. By introducing a band bending term, we realize two phase transitions, where a metallic phase emerges between the above two topological insulator phases. We discuss an electric-circuit realization of non-Hermitian non-Abelian topological insulators. We find that the spontaneous $PT$ symmetry breaking as well as the edge states are well observed by the impedance resonance.

arXiv comment8 pages, 7 figures

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• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
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• Demonstration of non-Abelian frame charge flow in photonic crystals
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• Floquet non-Abelian topological charges and edge states
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder