Phase Transitions in the Distribution of the Andreev Conductance of Superconductor-Metal Junctions with Multiple Transverse Modes
Kedar Damle, Satya N. Majumdar, Vikram Tripathi, Pierpaolo Vivo
DOI 10.1103/PhysRevLett.107.177206 · Physical Review Letters
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Abstract
We compute analytically the full distribution of Andreev conductance GNS of a metal-superconductor interface with a large number Nc of transverse modes, using a random matrix approach. The probability distribution P(GNS,Nc) in the limit of large Nc displays a Gaussian behavior near the average value ⟨GNS⟩=(2−2)Nc and asymmetric power-law tails in the two limits of very small and very large GNS. In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power-law tail for large GNS. Weakly nonanalytic points separate these four regimes—these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.
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