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Critical Current Calculations For Long $0$$pi$ Josephson Junction  Ivan Tornes
; David Stroud
;  Date: 
1 Nov 2007  Abstract:  A zigzag boundary between a $d_{x^2y^2}$ and an $s$wave superconductor is
believed to behave like a long Josephson junction with alternating sections of
$0$ and $pi$ symmetry. We calculate the fielddependent critical current of
such a junction, using a simple model. The calculation involves discretizing
the partial differential equation for the phase difference across a long
$0$$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 nonzero 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 previouslyobtained analytical superposition
result for $J_c(H_a)$. In the same limit, we also obtain an analytical
expression for the effective fielddependent quality factor $Q_J(H_a)$, finding
that $Q_J(H_a) propto sqrt{J_c(H_a)}$. We suggest that measuring the
fielddependence of $Q_J(H_a)$ would provide further evidence that this RCSJ
model applies to a long $0$$pi$ junction between a dwave and an swave
superconductor.  Source:  arXiv, 0711.0136  Services:  Forum  Review  PDF  Favorites 


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