Full counting statistics of multiple Andreev reflections

TL;DR

This paper derives the complete statistical distribution of charge transfer in a superconducting contact under voltage bias, revealing a multinomial process dominated by multiple Andreev reflections, with analytical results at zero temperature.

Contribution

It provides the first comprehensive derivation of full counting statistics for multiple Andreev reflections in superconducting point contacts of arbitrary transparency.

Findings

Charge transfer follows a multinomial distribution.

Analytical expressions for probabilities at zero temperature.

Results enable calculation of current, noise, and cumulants.

Abstract

We derive the full distribution of transmitted particles through a superconducting point contact of arbitrary transparency under voltage bias. The charge transport is dominated by multiple Andreev reflections. The counting statistics is a multinomial distribution of processes, in which multiple charges ne (n=1,2,3,...) are transferred through the contact. For zero temperature we obtain analytical expressions for the probabilities of the multiple Andreev reflections. The current, shot noise and high current cumulants in a variety of situations can be obtained from our result.