Dynamical Coulomb blockade of multiple Andreev reflections

TL;DR

This paper investigates how the dynamical Coulomb blockade affects multiple Andreev reflections in superconducting quantum point contacts, revealing a quadratic scaling at low transmission and potential current enhancement at higher transmission due to environmental coupling.

Contribution

It provides a detailed analysis of Coulomb blockade effects on MAR in superconducting contacts, including conditions for blockade and antiblockade phenomena, which were not previously characterized.

Findings

Blockade scales as n^2 at low transmission.

Higher transmission reduces blockade due to Pauli principle and elastic effects.

Under certain voltages, an antiblockade or current enhancement occurs.

Abstract

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as $n^2$ with $n = {Int}(2\Delta/eV)$, where $V$ is the bias voltage and $\Delta$ is the superconducting gap, as it would correspond to the occurrence of "shots" of charge $ne$. For higher transmission the blockade is reduced both due to Pauli principle and to elastic renormalization of the MAR probability, and for certain voltage regions it may even become an "antiblockade", i.e. the current is enhanced due to the coupling with the electromagnetic environment.