Influence of normal metal-superconductor interface on the statistics of conductance and shot noise power in a non-ideal chaotic quantum dot

Abstract

In this paper, we apply Andreev’s reflection to study the sub-gap coherent transport properties for a quantum dot attached to normal metal and superconductor reservoirs via non-ideal leads. We use the random matrix theory to obtain numerically the conductance and shot noise power probability densities varying the transparencies and the number of open scattering channels in each lead for the three Wigner–Dyson ensembles. We obtain results from the extreme quantum limit (where the conductance is of the order of 2e 2/h, the quantum of conductance) to the semiclassical regime (conductance much larger than 2e 2/h). We observe the appearance of non-analyticities in these probability densities and an interesting invariance break under the operation of exchanging the lead labels when time-reversal symmetry is absent.