推广的Su-Schrieffer-Heeger模型的拓扑相图及其表征拓扑相的有限尺度能谱和边界模

拓扑不变量如陈数、Z_2拓扑不变量等是表征拓扑非平庸固体系统的拓扑物相的特征量,其来源于固体周期边界条件下的能带即体能带所具有的不为零的Berry相.在开边界条件下,具有拓扑非平庸物相的系统的有限尺度能谱将出现位于能隙中的能带,并且这些能带可能对应着一个边界模.推广了一维Su-Schrieffer-Heeger模型,通过计算其拓扑不变量即Zak相,得到了其包含几个不同拓扑相的拓扑相图.在开边界条件下,研究了这些拓扑相对应的有限尺度能谱以及系统处于这些物相时能谱能隙中的能带所对应的边界模,进而采用有限尺度能谱和其能隙中的能带所对应的边界模表征了这些不同的拓扑相.

The topological phase diagrams of an extended Su-Schrieffer-Heeger model and energy spectra and edge modes of the finite-sized model as the representation of topological phases

The topological invariant, e.g. Chern number or Z_2 topological invariant characterizes the non-trivial properties of a topological phase in solids. It essentially stems from the non-zero Berry phase possessed by the bulk energy band of a solid under the periodic boundary condition. Under the open boundary condition, the energy spectrum of topological phase in the finite-sized lattice has bands in the energy gap, and these bands in the gap can correspond to the edge modes. In this study an extension of the one-dimensional Su-Schrieffer-Heeger was investigated. Its topological phase diagrams which possess several topologically non-trivia and trivial phases were obtained from the calculation of the topological invariant(in fact, under the periodic boundary condition). Under the open boundary condition, the energy spectra and the edge modes which correspond to the bands in gaps of these topologically non-trivial or trivial phase were obtained. These energy spectra and the edge modes distinguished the different topologically non-trivial phases and the topological transitions were indicated from the changes of the spectra and the patterns of edge modes.