Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice

TL;DR

This paper investigates the topological properties and mobility edges in a one-dimensional quasiperiodic p-wave superconductor using a modified real-space-Pfaffian method, revealing the protection of Majorana zero modes and the effects of disorder.

Contribution

It introduces a modified real-space-Pfaffian method for calculating topological invariants and explores the interplay between superconductivity and quasiperiodic disorder in 1D systems.

Findings

Majorana zero modes are topologically protected.

Mobility edges arise from competition between pairing and disorder.

Topological phase transitions involve energy gap closing and reopening.

Abstract

We aim to study a one-dimensional $p$-wave superconductor with quasiperiodic on-site potentials. A modified real-space-Pfaffian method is applied to calculate the topological invariants. We confirm that the Majorana zero mode is protected by the nontrivial topology the topological phase transition is accompanied by the energy gap closing and reopening. In addition, we numerically find that there are mobility edges which originate from the competition between the extended $p$-wave pairing and the localized quasi-disorder. We qualitatively analyze the influence of superconducting pairing parameters and on-site potential strength on the mobility edge. In general, our work enriches the research on the $p$-wave superconducting models with quasiperiodic potentials.