Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions

We study analytically a modified dimerized Kitaev chain model under both periodic and open boundary conditions and determine its phase diagram by calculating the topological number and edge correlation functions of Majorana fermions. We explicitly give analytical solutions for eigenstates of the model under open boundary conditions, which permit us to calculate two introduced edge correlation functions of Majorana fermions analytically. Our results indicate that the two edge correlation functions can be used to characterize the trivial, Su-Schrieffer-Heeger-like topological and topological superconductor phases. Furthermore, we find the existence of two different coupling patterns of Majorana fermions in topological superconductor phase characterized by different edge correlation functions, which can also be distinguished by investigating the survival probability of an edge Majorana under sudden quenching of parameters.