Coherent transport in Josephson-junction rhombi chain with quenched disorder

We consider a chain of Josephson-junction rhombi (proposed originally by Dou {{c}} {c}{}ot and Vidal) in the quantum regime. In the maximally frustrated case when magnetic flux through each rhombi Φᵣ is equal to one-half of the superconductive flux quantum Φ₀, 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 δΦ≡Φᵣ-Φ₀∕2>δΦᶜ from the maximally frustrated point brings the system back to the usual $2e$-quantized supercurrent. For a regular chain δΦᶜ 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 δΦᶜ.