Universal Conductance Fluctuations in Mesoscopic Systems with Superconducting Leads: Beyond the Andreev Approximation

TL;DR

This study investigates universal conductance fluctuations in mesoscopic normal metal-superconductor systems, revealing how electron-hole degeneracy influences conductance variability and distribution, especially within the superconducting gap and in different transport regimes.

Contribution

It demonstrates the role of electron-hole degeneracy in classifying universal conductance fluctuations and characterizes conductance distributions across regimes beyond the Andreev approximation.

Findings

UCF in the superconducting gap is about twice that in normal systems.

Electron-hole degeneracy determines the universality class of conductance fluctuations.

Conductance distribution depends only on ehD and is universal for fixed average conductance.

Abstract

We report our investigation of the sample to sample fluctuation in transport properties of phase coherent normal metal-superconductor hybrid systems. Extensive numerical simulations were carried out for quasi-one dimensional and two dimensional systems in both square lattice (Fermi electron) as well as honeycomb lattice (Dirac electron). Our results show that when the Fermi energy is within the superconducting energy gap $\Delta$, the Andreev conductance fluctuation exhibits a universal value (UCF) which is approximately two times larger than that in the normal systems. According to the random matrix theory, the electron-hole degeneracy (ehD) in the Andreev reflections (AR) plays an important role in classifying UCF. Our results confirm this. We found that in the diffusive regime there are two UCF plateaus, one corresponds to the complete electron-hole symmetry (with ehD) class and the other to conventional electron-hole conversion (ehD broken). In addition, we have studied the Andreev conductance distribution and found that for the fixed average conductance $,G>$ the Andreev conductance distribution is a universal function that depends only on the ehD. In the localized regime, our results show that ehD continues to serve as an indicator for different universal classes. Finally, if normal transport is present, i.e., Fermi energy is beyond energy gap $\Delta$, the AR is suppressed drastically in the localized regime by the disorder and the ehD becomes irrelevant. As a result, the conductance distribution is that same as that of normal systems.