Eur. Phys. J. B 59, 485-493 (2007)
https://doi.org/10.1140/epjb/e2007-00309-x

Critical current calculations for long 0-π Josephson junctions

Department of Physics, Ohio State University, Columbus, OH, 43210, USA

Corresponding author: ^a stroud@mps.ohio-state.edu

Received: 14 April 2007
Revised: 2 September 2007
Published online: 15 November 2007

Abstract

A zigzag boundary between a d_x²-y² and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J_c(H_a) is maximum at non-zero applied magnetic field H_a, and depends strongly on the ratio of Josephson penetration depth λ_J to facet length L_f. If λ_J/L_f ≫1 and the number of facets is large, there is a broad range of H_a where J_c(H_a) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ_J/L_f →∞, our model reduces to a previously-obtained analytical superposition result for J_c(H_a). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q_J(H_a), finding that . We suggest that measuring the field-dependence of Q_J(H_a) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.