Generalized Eilenberger theory for Majorana zero-mode-carrying disordered $p$-wave superconductors

TL;DR

This paper extends Eilenberger theory to analyze how disorder affects Majorana zero modes in p-wave superconductors, revealing that zero-bias peaks can persist even after the superconducting gap closes due to disorder.

Contribution

It introduces a generalized Eilenberger framework that includes spatial dependence of Majorana wave functions to study disorder effects.

Findings

Majorana modes become delocalized with increasing disorder.

Zero bias peaks can survive beyond the gap-closing point.

Disorder suppresses the superconducting gap but does not necessarily eliminate Majorana signatures.

Abstract

Disorder is known to suppress the gap of a topological superconducting state that would support non-Abelian Majorana zero modes. In this paper, we study using the self-consistent Born approximation the robustness of the Majorana modes to disorder within a suitably extended Eilenberger theory, in which the spatial dependence of the localized Majorana wave functions is included. We find that the Majorana mode becomes delocalized with increasing disorder strength as the topological superconducting gap is suppressed. However, surprisingly, the zero bias peak seems to survive even for disorder strength exceeding the critical value necessary for closing the superconducting gap within the Born approximation.