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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(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低带、局域在系统一侧的边缘态，另一种是出现在第二条和第三条能带中间、局域性相对较弱的边缘态，且不会进入到能隙中。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 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.
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Keywords:
- T-graphene structure /
- PT symmetry /
- Energy spectra /
- Edge states
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