AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL

TL;DR

This paper calculates the current components in a short 1D superconducting channel, revealing how the Josephson effect transitions from phase evolution to multiple Andreev reflections, with a focus on high transparency and Landau-Zener transitions.

Contribution

It provides a comprehensive analysis of current behavior in a quantum channel between superconductors, highlighting the crossover mechanisms and the persistent current-phase relation at high transparency.

Findings

In the ballistic limit, the crossover is described by Landau-Zener transitions.

The stationary current-phase relation is not recovered at perfect transmission.

The current follows a  \\sin /2 b7 sign V relation at small voltages.

Abstract

We have calculated all the components of the current in a short one-dimensional channel between two superconductors for arbitrary voltages and transparencies $D$ of the channel. We demonstrate that in the ballistic limit ($D\simeq 1$), the crossover between the quasistationary evolution of the Josephson phase difference $\varphi$ at small voltages and transport by multiple Andreev reflections at larger voltages can be described as the Landau-Zener transition induced by finite reflection in the channel. For perfect transmission and vanishing energy relaxation rate the stationary current-phase relation is never recovered, and $I(\varphi)=I_c \mid \sin \varphi /2 \mid \mbox{sign} V$ for arbitrary small voltages.