Adiabatic pumping in a Superconductor-Normal-Superconductor weak link

TL;DR

This paper develops a formalism to analyze adiabatic charge pumping in superconductor-normal-superconductor junctions, linking the pumped charge to Berry phase and distinguishing it from Josephson current.

Contribution

It introduces a new formalism connecting adiabatic pumping to Berry phase in SNS junctions, especially for short normal regions, and clarifies the phase dependence of pumped charge.

Findings

Pumped charge is related to Berry phase of Andreev states.

Pumped charge is an even function of the superconducting phase difference.

The formalism distinguishes pumped charge from Josephson current.

Abstract

We present a formalism to study adiabatic pumping through a superconductor - normal - superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.