Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain

Abstract

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 investigate a non- Hermitian finite-size Kitaev chain with PT-symmetric chemical potentials. Exact solution at the symmetric point shows that Majorana edge modes can emerge as the coalescing states at exceptional points and PT symmetry breaking states. The coalescing zero mode is the finite-size projection of the conventional degenerate zero modes in a Hermitian infinite system with the open boundary condition. It indicates a 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.