Noise and Full Counting Statistics of Incoherent Multiple Andreev Reflection

TL;DR

This paper develops a comprehensive stochastic theory for full counting statistics in incoherent multiple Andreev reflections, revealing subharmonic gap structures and divergent higher cumulants at low voltages in superconductor-normal-superconductor contacts.

Contribution

It introduces a general stochastic path integral framework for analyzing full counting statistics in incoherent MAR, including new low-voltage behavior insights.

Findings

All current cumulants show subharmonic gap structures at specific voltages.

At low voltages, cumulants scale as powers of voltage, diverging for higher orders.

The low-voltage behavior applies broadly to various incoherent SNS contacts.

Abstract

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages $V=2\Delta/en$. For low voltages $V\ll\Delta/e$, the counting statistics results from diffusion of multiple charges in energy space, giving the $p$th cumulant $<Q^p> \propto V^{2-p}$, diverging for $p\geq 3$. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.