Li C, Jin L, Song Z
Department of Physics, University of Hong Kong, Hong Kong, China.
School of Physics, Nankai University, Tianjin, 300071 China.
Sci Rep. 2020 Apr 22;10(1):6807. doi: 10.1038/s41598-020-63369-x.
A single unit cell contains all the information about the bulk system, including the topological feature. The topological invariant can be extracted from a finite system, which consists of several unit cells under certain environment, such as a non-Hermitian external field. We present an exact solvable non-Hermitian finite-size Kitaev chain with -symmetric chemical potentials at the symmetric point. The straightforward calculation shows that there are two kinds of Majorana edge modes in this model divided by symmetry-broken and unbroken. The one appeared in the symmetry-unbroken region can be seen as the finite-size projection of the conventional degenerate zero modes in a Hermitian infinite system with the open boundary condition. It indicates a possible variant of the bulk-edge correspondence: The number of Majorana edge modes in a finite non-Hermitian system can be the topological invariant to identify the topological phase of the corresponding bulk Hermitian system.
一个单胞包含了关于整个系统的所有信息，包括拓扑特征。拓扑不变量可以从一个有限系统中提取，该有限系统由在特定环境下（如非厄米外场）的几个单胞组成。我们提出了一个在对称点具有 - 对称化学势的精确可解非厄米有限尺寸基塔耶夫链。直接计算表明，在这个模型中，根据对称性破缺和未破缺可分为两种马约拉纳边缘模式。出现在对称性未破缺区域的那种模式可以看作是具有开放边界条件的厄米无限系统中传统简并零模的有限尺寸投影。这表明了体边对应关系的一种可能变体：有限非厄米系统中马约拉纳边缘模式的数量可以作为识别相应体厄米系统拓扑相的拓扑不变量。
