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

Abstract

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