Superconducting $p$-wave pairing effects on one-dimensional non-Hermitian quasicrystals with power law hopping

TL;DR

This paper investigates how superconducting p-wave pairing influences the topological and localization properties of a non-Hermitian Aubry-André-Harper model with power-law hopping, revealing new edge states and phase diagram features.

Contribution

It introduces the effects of p-wave pairing on non-Hermitian quasicrystals with power-law hopping, highlighting the emergence of Majorana and Dirac modes and their localization behaviors.

Findings

Weak pairing induces oscillating quasi-Majorana modes.

Strong pairing localizes Majorana and Dirac modes at edges.

Superconducting pairing reduces fractal dimension plateaus.

Abstract

We study the effects of superconducting $p$-wave pairing on the non-Hermitian Aubry-Andr\'e-Harper model with power-law hopping. For the case of short-range hopping, weak pairing leads to oscillating quasi-Majorana zero modes, turning to edge-localized Majorana zero modes as pairing strength increases. For the case of long-range hopping, we observe the emergence of massive Dirac modes having oscillatory behavior, similar to Majorana modes with weak pairing. The massive Dirac modes localize at the edges as the pairing strength grows. The superconducting pairing spoils the plateaus observed in the fractal dimension of all the energy eigenstates of the Aubry-Andr\'e-Harper model with power-law hopping. The number of plateaus decreases with the increasing pairing strength for the weak non-Hermiticity in the system. The phase diagram of the system reveals that real and complex energy spectrums correlate differently with the localization properties of the eigenstates depending on the strength of pairing and hopping range.