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

This paper investigates the regulatory effect of non-Hermitian mechanisms on energy spectra and edge states by applying a single- or double-layer imaginary potential with parity-time (PT) symmetry to both sides of the T-graphene ribbon. The findings indicate that the type of imaginary potential applied has a significant modulation effect on the energy band structure and localization of the system. Specifically, when an imaginary potential is applied to the outermost monolayer lattice point of the ribbon, the energy of the edge state appears in the imaginary part. For its probability density distribution, its locality changes from both-sided to one-sided locality, and becomes stronger with the increase of imaginary potential. Additionally, the PT symmetry phase transition occurs in the topologically trivial region. Notably, as the imaginary potential reaches a critical value, new imaginary-energy edge state emerges within the bulk state energy gap and also shows 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 band and the bottom band, localized on one side of the system. The second type emerges in the middle of the second energy band and the third energy band, displaying relatively weak localization and not penetrating the energy gap. This work contributes to understanding the regulatory effect of the edge imaginary potential of PT symmetry on the physical properties of T-graphene structures.