Random-matrix theory of Andreev reflection from a topological superconductor

TL;DR

This paper uses random-matrix theory to analyze how the topological quantum number influences Andreev reflection and conductance distributions in topological superconductors, revealing nonperturbative effects and phase-dependent conductance characteristics.

Contribution

It provides a detailed statistical analysis of Andreev reflection eigenvalues and conductance distributions, highlighting the nonperturbative dependence on topological quantum number Q.

Findings

Conductance cumulants of order p<N/d are independent of Q.

Full conductance distribution P(G) differs qualitatively between trivial and nontrivial phases.

Large-N effects like weak localization do not reveal topological quantum numbers.

Abstract

We calculate the probability distribution of the Andreev reflection eigenvalues R_n 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.