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

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.

10 pages, 5 figures

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Cited by in corpus (4)

• Tunneling transport in NSN junctions made of Majorana nanowires across the topological quantum phase transition
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Long range $p$-wave proximity effect into a disordered metal
• Enhanced zero-bias conductance peak and splitting at mesoscopic interfaces between an $s$-wave superconductor and a 3D Dirac semimetal