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03 November 2024
 
  » arxiv » 0711.0136

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Critical Current Calculations For Long $0$-$pi$ Josephson Junction
Ivan Tornes ; David Stroud ;
Date 1 Nov 2007
AbstractA zigzag boundary between a $d_{x^2-y^2}$ and an $s$-wave superconductor is believed to behave like a long Josephson junction with alternating sections of $0$ and $pi$ 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 $0$-$pi$ junction. In this form, the equations describe a hybrid ladder of inductively coupled small $0$ and $pi$ 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 $lambda_J$ to facet length $L_f$. If $lambda_J/L_f gg 1$ 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 $lambda_J/L_f o infty$, 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 $Q_J(H_a) propto sqrt{J_c(H_a)}$. We suggest that measuring the field-dependence of $Q_J(H_a)$ would provide further evidence that this RCSJ model applies to a long $0$-$pi$ junction between a d-wave and an s-wave superconductor.
Source arXiv, 0711.0136
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