Mesoscopic conductance fluctuations and noise in disordered Majorana wires

TL;DR

This paper investigates the transport properties and conductance fluctuations of disordered topological superconducting wires at the critical transition point, revealing how disorder influences Majorana states and conductance statistics.

Contribution

It develops a supersymmetric sigma model approach to analyze conductance and noise in disordered Majorana wires across different length regimes, including the critical transition.

Findings

Derived average conductance and its variance across wire lengths

Calculated shot noise power and topological index fluctuations

Identified conductance distribution broadening beyond the correlation length

Abstract

Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length $L$ of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of $L$ from the Ohmic limit of short wires to the regime of a broad conductance distribution when $L$ exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary $L$. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.