Phases of Josephson Junction Ladders

TL;DR

This paper investigates the phase behavior of Josephson junction ladders under magnetic fields using transfer matrix methods, revealing complex phase structures and a superconducting-normal transition influenced by coupling variations.

Contribution

It introduces a transfer matrix approach to analyze phase diagrams of Josephson ladders, highlighting the devil's staircase structure and a continuous transition in the transverse direction.

Findings

Eigenvalues determine distinct phases of the ladder.

Ground state exhibits devil's staircase as a function of flux.

Continuous superconducting-normal transition observed with coupling variation.

Abstract

We study a Josephson junction ladder in a magnetic field in the absence of charging effects via a transfer matrix formalism. The eigenvalues of the transfer matrix are found numerically, giving a determination of the different phases of the ladder. The spatial periodicity of the ground state exhibits a devil's staircase as a function of the magnetic flux filling factor $f$. If the transverse Josephson coupling is varied a continuous superconducting-normal transition in the transverse direction is observed, analogous to the breakdown of the KAM trajectories in dynamical systems.