Critical current calculations for long 0-π Josephson junctions
Department of Physics, Ohio State University, Columbus, OH, 43210, USA
Corresponding author: a email@example.com
Revised: 2 September 2007
Published online: 15 November 2007
A zigzag boundary between a dx2-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 Jc(Ha) is maximum at non-zero applied magnetic field Ha, and depends strongly on the ratio of Josephson penetration depth λJ to facet length Lf. If λJ/Lf ≫1 and the number of facets is large, there is a broad range of Ha where Jc(Ha) 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 λJ/Lf →∞, our model reduces to a previously-obtained analytical superposition result for Jc(Ha). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor QJ(Ha), finding that . We suggest that measuring the field-dependence of QJ(Ha) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.
PACS: 74.50.+r – Tunneling phenomena; point contacts, weak links, Josephson effects / 74.81.Fa – Josephson junction arrays and wire networks / 74.20.Rp – Pairing symmetries (other than s-wave)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007