Coherent transport in Josephson-Junction rhombi chain with quenched disorder

TL;DR

This paper analyzes how quenched disorder affects the coherent pair transport in a Josephson-junction rhombi chain, especially the transition from 4e to 2e supercurrent quantization under magnetic flux deviations.

Contribution

It provides a detailed analysis of the impact of quenched disorder on the pairing supercurrent in a Josephson-junction rhombi chain, extending previous work on regular chains.

Findings

Disorder suppresses the 4e pairing supercurrent.

Critical flux deviation  is affected by disorder.

Disorder can restore 2e supercurrent even at maximal frustration.

Abstract

We consider a chain of Josephson-junction rhombi (proposed originally by Doucot and Vidal) in quantum regime. In a regular chain with no disorder in the maximally frustrated case when magnetic flux through each rhombi \Phi_r is equal to one half of superconductive flux quantum \Phi_0, Josephson current is due to correlated transport of pairs of Cooper pairs, i.e. charge is quantized in units of $4e$. Sufficiently strong deviation \delta\Phi =|\Phi_r-\Phi_0/2| > \delta\Phi^c from the maximally frustrated point brings the system back to usual $2e$-quantized supercurrent. For a regular chain \delta\Phi^c was calculated by us previously. Here we present detailed analysis of the effect of quenched disorder (random stray charges and random fluxes piercing rhombi) on the pairing effect.