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

TL;DR

This paper explores how Majorana edge modes in a non-Hermitian PT-symmetric Kitaev chain can be characterized by topological invariants derived from finite systems, revealing a new bulk-edge correspondence in non-Hermitian topological phases.

Contribution

It demonstrates that Majorana edge modes in a finite non-Hermitian Kitaev chain emerge as coalescing states at exceptional points, establishing a novel bulk-edge correspondence.

Findings

Majorana modes appear as coalescing states at exceptional points.

The number of Majorana modes serves as a topological invariant.

Finite-size analysis reveals a bulk-edge correspondence in non-Hermitian systems.

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.