Superconducting states and depinning transitions of Josephson ladders

TL;DR

This paper analyzes the stability and transitions of superconducting states in Josephson ladder arrays, providing analytical approximations, bifurcation-based depinning currents, and stability diagrams considering edge effects.

Contribution

It introduces analytical methods for pinned states in Josephson ladders, incorporating edge effects and deriving stability criteria and phase diagrams.

Findings

Analytical approximations for superconducting states as functions of current and frustration.

Formulas for depinning currents and critical frustrations at bifurcations.

Comparison of edge-influenced stability diagrams with thermodynamic phase diagrams.

Abstract

We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states -- the no-vortex, fully-frustrated and single-vortex states -- as functions of the dc bias current $I$ and the frustration $f$. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as $I$ and $f$ are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to $I$ and $f$. To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances.