Discontinuous current-phase relations in small 1D Josephson junction arrays

TL;DR

This paper investigates the current-phase relationships in small 1D Josephson junction arrays, revealing persistent discontinuities at phase π and providing analytical models for larger systems near charge degeneracy.

Contribution

It introduces a detailed analysis of current-phase relations in small 1D Josephson arrays, including analytical solutions for larger arrays near charge degeneracy.

Findings

Discontinuities in IΦ at phase π persist in small arrays.

Charge degeneracy lines influence the current-phase relationship.

Analytical mapping to a tight-binding model for large arrays.

Abstract

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase relationships (I$\Phi$). We present results for a three-junction system in the vicinity of charge degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I$\Phi$ at phase $\pi$ persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.