Non-Hermitian non-Abelian topological insulators with PT symmetry

Abstract

We study a non-Hermitian non-Abelian topological insulator preserving symmetry, where the non-Hermitian term represents nonreciprocal hoppings. As it increases, a spontaneous 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 symmetry breaking as well as the edge states are well observed by the impedance resonance.