具有宇称-时间反演对称性的虚势能对T-型石墨烯结构能谱和边缘态的影响  

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

作　　者：江翠[1] 李家锐 亓迪 张莲莲[2] Jiang Cui;Li Jia-Rui;Qi Di;Zhang Lian-Lian(Basic Department,Shenyang Institute of Engineering,Shenyang 110136,China;College of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]沈阳工程学院基础部,沈阳110136 [2]东北大学理学院,沈阳110819

出　　处：《物理学报》2024年第20期253-265,共13页Acta Physica Sinica

基　　金：辽宁省自然科学基金(批准号:2023-MSLH-218);国家自然科学基金(批准号:11905027)资助的课题.

摘　　要：本文通过T-型石墨烯结构的条带两侧分别施加单层或者双层具有宇称-时间(parity-time,PT)对称性的虚势能,考察了非厄米机制对能谱和边缘态的调控作用.结果发现,当对条带最外侧单层格点施加虚势能时,边缘态的能量出现虚部,并且从局域在系统两侧变为一侧.而拓扑平庸区出现PT对称相转变.当虚势能达到临界值时,体态的能隙中会有新的虚能边缘态.另一方面,当施加双层虚势能时,体系中会出现两种不同的边缘态.一种是出现在顶带和底带、局域在系统一侧的边缘态,另一种是出现在第2条和第3条能带中间、局域性相对较弱的边缘态,且不会进入能隙中.本工作有助于理解PT对称的边缘虚势能对T-型石墨烯结构物性的调控作用.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.

关 键 词：T-型石墨烯结构 宇称-时间对称 能谱 边缘态 

分 类 号：O469[理学—凝聚态物理]