Random-matrix theory of Andreev reflection from a topological superconductor

C. W. J. Beenakker; J. P. Dahlhaus; M. Wimmer; A. R. Akhmerov

doi:10.1103/PhysRevB.83.085413

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Random-matrix theory of Andreev reflection from a topological superconductor

C. W. J. Beenakker, J. P. Dahlhaus, M. Wimmer, A. R. Akhmerov

DOI 10.1103/PhysRevB.83.085413 · Physical Review B

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Abstract

We calculate the probability distribution of the Andreev reflection eigenvalues Rn at the Fermi level in the circular ensemble of random-matrix theory. Without spin-rotation symmetry, the statistics of the electrical conductance G depends on the topological quantum number Q of the superconductor. We show that this dependence is nonperturbative in the number N of scattering channels by proving that the p-th cumulant of G is independent of Q for p<N/d (with d=2 or d=1 in the presence or in the absence of time-reversal symmetry). A large-N effect such as weak localization cannot, therefore, probe the topological quantum number. For small N we calculate the full distribution P(G) of the conductance and find qualitative differences in the topologically trivial and nontrivial phases.