Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes

TL;DR

This paper analytically derives the full distribution of Andreev conductance in superconductor-metal junctions with many modes, revealing phase transitions and distinct regimes in the conductance distribution.

Contribution

It introduces a random matrix approach to compute the conductance distribution and uncovers phase transitions in the associated Coulomb gas model.

Findings

Distribution exhibits Gaussian core with power-law tails.

Discovery of a novel intermediate regime for large conductance.

Identification of phase transitions causing non-analytic points.

Abstract

We compute analytically the full distribution of Andreev conductance $G_{\mathrm{NS}}$ of a metal-superconductor interface with a large number $N_c$ of transverse modes, using a random matrix approach. The probability distribution $\mathcal{P}(G_{\mathrm{NS}},N_c)$ in the limit of large $N_c$ displays a Gaussian behavior near the average value $<G_{\mathrm{NS}}>= (2-\sqrt{2}) N_c$ and asymmetric power-law tails in the two limits of very small and very large $G_{\mathrm{NS}}$. In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power law tail for large $G_{\mathrm{NS}}$. Weakly non-analytic points separate these four regimes---these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.