Higher-order mesoscopic fluctuations in quantum wires: Conductance and current cumulants

TL;DR

This paper investigates higher-order conductance and current cumulants in mesoscopic quantum wires, revealing nonanalytic length dependencies and providing new scaling forms, especially in the Bogoliubov--de Gennes symmetry class.

Contribution

It introduces a unified recursion equation for conductance cumulants across symmetry classes and uncovers nonanalytic length dependencies for higher-order cumulants in BdG wires.

Findings

Higher-order conductance cumulants exhibit nonanalytic length dependence.

A novel scaling form for conductance cumulants is proposed.

Weak-localization corrections to current cumulants up to order 10 are calculated.

Abstract

We study conductance cumulants $<< g^n >>$ and current cumulants $C_j$ related to heat and electrical transport in coherent mesoscopic quantum wires near the diffusive regime. We consider the asymptotic behavior in the limit where the number of channels and the length of the wire in the units of the mean free path are large but the bare conductance is fixed. A recursion equation unifying the descriptions of the standard and Bogoliubov--de Gennes (BdG) symmetry classes is presented. We give values and come up with a novel scaling form for the higher-order conductance cumulants. In the BdG wires, in the presence of time-reversal symmetry, for the cumulants higher than the second it is found that there may be only contributions which depend nonanalytically on the wire length. This indicates that diagrammatic or semiclassical pictures do not adequately describe higher-order spectral correlations. Moreover, we obtain the weak-localization corrections to $C_j$ with $j\le 10$.