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.
Highlights
Topological insulators are one of the most fascinating ideas in contemporary physics [1,2]
We show that a spontaneous PT symmetry breaking is induced by increasing the nonreciprocal hoppings from a phase transition
We proposed a non-Hermitian non-Abelian topological insulator model by imposing PT symmetry in one dimension
Summary
Topological insulators are one of the most fascinating ideas in contemporary physics [1,2]. Non-Abelian topological numbers have been discussed in three-band models protected by PT symmetry [3,4,5,6,7] or C2T symmetry [8,9] They were realized in nodal line semimetals [3,4,6,7,10,11,12] in three dimensions and Weyl points [8] in two dimensions. There is a PT symmetry breaking transition, where the eigenvalues and eigenfunctions become complex Nonreciprocal hopping is such a hopping that the right-going and left-going hopping amplitude are different [37]. We study a non-Hermitian non-Abelian topological insulator in an N band model with PT symmetry. The edge states and the spontaneous PT symmetry breaking are found to be well signaled by the impedance resonance
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