On the non-hermitian Kitaev chain

TL;DR

This paper analyzes the non-Hermitian Kitaev chain, providing a novel method to characterize eigenvalue curves, conditions for the skin effect absence, and the parameter space for zero modes, advancing understanding of non-Hermitian topological systems.

Contribution

It introduces a new method to characterize eigenvalues in non-Hermitian systems and fully determines conditions for skin effect absence and zero modes in the non-Hermitian Kitaev chain.

Findings

Eigenvalue curves in the complex plane are characterized in the infinite size limit.

Conditions for the absence of the skin effect are identified.

Parameter regions with zero modes are fully determined.

Abstract

We study the non-hermitian Kitaev chain model, for arbitrary complex parameters. In particular, we give a concise characterisation of the curves of eigenvalues in the complex plane in the infinite size limit, using a novel method which can be applied to other non-hermitian systems. Using this solution, we characterise under which conditions the skin effect is absent, and for which eigenstates this is the case. We also fully determine the region in parameter space for which the model has a zero mode.