Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices

TL;DR

This paper investigates a non-Hermitian quasiperiodic p-wave superconductor, demonstrating the robustness of Majorana zero modes, topological phase transitions linked to localization, and a unique real-complex energy spectrum transition.

Contribution

It provides an analytic topological phase boundary, explores the interplay between topology and localization, and uncovers a novel real-complex spectral transition in non-Hermitian quasiperiodic systems.

Findings

Majorana zero modes remain robust despite non-Hermiticity.

Topological phase transition coincides with Anderson localization transition.

Discovery of a non-conventional real-complex energy spectrum transition.

Abstract

We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non-Hermitian quasiperiodic potentials. Finally, we numerically uncover a non-conventional real-complex transition of the energy spectrum, which is different from the conventional $\mathcal{PT}$ symmetric transition.