Investigating topological in-gap states in non-Hermitian quasicrystal with unconventional $p$-wave pairing

TL;DR

This paper investigates topological in-gap states in a non-Hermitian quasicrystal with unconventional p-wave pairing, revealing robust in-gap states under open boundary conditions that could be useful for topological quantum computing.

Contribution

It introduces a non-Hermitian Aubry-André-Harper model with p-wave pairing considering onsite non-Hermiticity, discovering new in-gap states with topological protection.

Findings

Identifies triple-phase transitions including topological and metal-insulator transitions.

Observes in-gap states under open boundary conditions that are robust against disorder.

Contrasts these states with Majorana zero modes, highlighting their potential for quantum computing.

Abstract

The interplay of onsite quasiperiodic potential, superconductivity, and non-Hermiticity is explored in a non-Hermitian unconventional superconducting quasicrystal described by Aubry-Andr\'e-Harper (NHAAH) model with $p$-wave pairing. In previous studies, the non-Hermiticity was only considered at the onsite quasiperiodic potential of the NHAAH model, and Majorana zero modes (MZMs) were observed under open boundary conditions (OBC) in this model. In this work, we study an NHAAH model with $p$-wave pairing, where non-Hermiticity is considered onsite by introducing complex quasiperiodic potential and asymmetry at the hopping part. Our analysis uncovers triple-phase transitions, where topological, metal-insulator, and unconventional real-to-complex transitions coincide at weak $p$-wave pairing strength. Additionally, instead of the MZMs observed in the symmetric hopping case, we observe the emergence of in-gap states under OBC in this model. These in-gap states are robust against disorder, underscoring their topological protection. Therefore, unlike the MZMs, which are very challenging to experimentally realize, these in-gap states can be used in topological quantum computational protocols.