Effect of imaginary potential energy with parity-time symmetry on the band structures and edge states of T-graphene

Abstract

This paper investigates the regulatory effect of non-Hermitian mechanisms on energy spectra and edge states by applying a single or double layer of imaginary potentials with PT symmetry on both sides of the T-graphene ribbon. The findings indicate that the type of imaginary potential application has a significant modulation effect on the energy band structure and localization of the system. Specifically, when the imaginary potentials are applied to the outermost monolayer lattice point of the ribbon, the energy of the edge states appears in the imaginary part. For its probability density distribution, its locality changes from being localized on both sides to one side and becomes stronger with the increase of imaginary potentials. Additionally, the PT symmetry phase transition occurs in the topologically trivial region. Notably, as the imaginary potentials reach a critical value, new imaginary-energy edge states emerge within the bulk state energy gap and also show the phenomenon that the localization is on one side of the system. Furthermore, when double-layer imaginary potentials are applied, two different edge states will appear in the system. The first type appears in the top and bottom bands, localized on one side of the system. The second type emerges in the middle of the second and third energy bands, displaying relatively weak localization and not penetrating the energy gap. This work helps to understand the regulatory effect of the edge imaginary potentials of PT symmetry on the physical properties of T-graphene structures.