Size Effects on the Conditions of Edge State Formation in 1D Systems

A criterion for revealing edge states in the case when the size of a system is comparable with the localization length of these states has been proposed. The application of the algorithm for determining edge states in short systems has been demonstrated on examples of the Bernevig–Hughes–Zhang (BHZ) model in the cylindrical geometry, the Kitaev model, and a chain with the spin–orbit interaction and induced superconductivity. It has been shown that for finite-length 1D systems, there exist ranges of parameters in which the edge states are not formed, although the topological index is nontrivial; conversely, the emergence of the Majorana modes in regions with a trivial topological index has been demonstrated.