Equilibrium properties of a Josephson-junction ladder with screening effects

Abstract

We calculate the ground-state phase diagram of a Josephson-junction ladder when screening field effects are taken into account. We study the ground-state configuration as a function of the external field, the penetration depth, and the anisotropy of the ladder, using different approximations to the calculation of the induced fields. A series of tongues, characterized by the vortex density ω, is obtained. The vortex density of the ground state, as a function of the external field, is a devil’s staircase, with a plateau for every rational value of ω. The width of each of these steps depends strongly on the approximation made when calculating the inductance effect: If the self-inductance matrix is considered, the ω=0 phase tends to occupy all the diagram as the penetration depth decreases. If, instead, the whole inductance matrix is considered, the width of any step tends to a nonzero value in the limit of very low penetration depth. We have also analyzed the stability of some simple metastable phases: Screening fields are shown to enlarge their stability range. © 1996 The American Physical Society.

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