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

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

2011-06-06

arxiv.org/abs/1106.0980v2

Phys. Rev. Lett. 107, 177206 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 fig. Minor changes. Published version

Scientific paper

10.1103/PhysRevLett.107.177206

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 $= (2-\sqrt{2}) N_c$ 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.

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