Coherent transport in Josephson-junction rhombi chain with quenched disorder

Abstract

We consider a chain of Josephson-junction rhombi (proposed originally by Dou\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ot and Vidal) in the quantum regime. In the maximally frustrated case when magnetic flux through each rhombi ${\ensuremath{\Phi}}_{r}$ is equal to one-half of the superconductive flux quantum ${\ensuremath{\Phi}}_{0}$, the Josephson current is due to the correlated transport of pairs of Cooper pairs; i.e., charge is quantized in units of $4e$. A sufficiently strong deviation $\ensuremath{\delta}\ensuremath{\Phi}\ensuremath{\equiv}\ensuremath{\mid}{\ensuremath{\Phi}}_{r}\ensuremath{-}{\ensuremath{\Phi}}_{0}∕2\ensuremath{\mid}>\ensuremath{\delta}{\ensuremath{\Phi}}^{c}$ from the maximally frustrated point brings the system back to the usual $2e$-quantized supercurrent. For a regular chain $\ensuremath{\delta}{\ensuremath{\Phi}}^{c}$ was calculated by us in Phys. Rev. B 70, 184519 (2004). Here we present a detailed analysis of the effect of quenched disorder (random stray charges and random fluxes piercing rhombi) on the pairing effect. For the case of a chain with random stray charges in the quantum regime we derive the probability to find the system in the $4e$-dominated regime and estimate the characteristic value of the critical deflection $\ensuremath{\delta}{\ensuremath{\Phi}}^{c}$.