Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

TL;DR

This paper investigates a non-Hermitian quasiperiodic p-wave superconductor, revealing real-complex energy transitions, a correspondence between energy types and state localization, and the robustness of Majorana zero modes against non-Hermiticity.

Contribution

It uncovers the existence of real-complex energy transitions without PT-symmetry breaking and links energy types to state localization, advancing understanding of topological properties in non-Hermitian systems.

Findings

Real-complex energy transition occurs without PT-symmetry breaking.

Pure real energies correspond to extended states, complex energies to localized states.

Majorana zero modes are immune to non-Hermiticity.

Abstract

In this paper, a one-dimensional non-Hermitian quasiperiodic $p$-wave superconductor without $\mathcal{PT}$-symmetry is studied. By analyzing the spectrum, we discovered there still exists real-complex energy transition even if the inexistence of $\mathcal{PT}$-symmetry breaking. By the inverse participation ratio, we constructed such a correspondence that pure real energies correspond to the extended states and complex energies correspond to the localized states, and this correspondence is precise and effective to detect the mobility edges. After investigating the topological properties, we arrive at a fact that the Majorana zero modes in this system are immune to the non-Hermiticity.