Theory of 4e versus 2e supercurrent in frustrated Josepshon-junction rhombi chain

TL;DR

This paper analyzes the transition between 4e and 2e supercurrent in a chain of Josephson junction rhombi, focusing on how magnetic flux deviation influences the quantization of supercurrent in the quantum regime.

Contribution

It provides a detailed theoretical analysis of the conditions under which 4e supercurrent dominates and how deviations from maximal frustration restore 2e supercurrent, including parameter estimates for experimental observation.

Findings

4e supercurrent occurs at maximal frustration with flux  of flux quantum.

Deviations  from maximal frustration revert supercurrent to 2e quantization.

Analysis covers fluctuation-dominated regime, chain length, and energy ratios.

Abstract

We consider a chain of Josepshon-junction rhombi (proposed originally in \cite{Doucot}) in quantum regime, and in the realistic case when charging effects are determined by junction capacitances. In the maximally frustrated case when magnetic flux through each rhombi $\Phi_r$ is equal to one half of superconductive flux quantum $\Phi_0$, Josepshon current is due to correlated transport of {\em pairs of Cooper pairs}, i.e. charge is quantized in units of $4e$. Sufficiently strong deviation $ \delta\Phi \equiv |\Phi_r-\Phi_0/2| > \delta\Phi^c$ from the maximally frustrated point brings the system back to usual $2e$-quantized supercurrent. We present detailed analysis of Josepshon current in the fluctuation-dominated regime (sufficiently long chains) as function of the chain length, $E_J/E_C$ ratio and flux deviation $ \delta\Phi$. We provide estimates for the set of parameters optimized for the observation of $4e$-supercurrent.