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

TL;DR

This paper investigates a non-Hermitian non-Abelian topological insulator with $PT$ symmetry, revealing phase transitions, spontaneous symmetry breaking, and potential realization in electric circuits through impedance resonance.

Contribution

It introduces a new non-Hermitian non-Abelian topological insulator model with $PT$ symmetry, analyzing phase transitions and experimental detection methods.

Findings

Spontaneous $PT$ symmetry breaking transition occurs in the model.

Two phase transitions with a metallic phase between topological phases.

Edge states are observable via impedance resonance in electric circuits.

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.