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Article overview
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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 $d_{x^2-y^2}$ 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 | Services: | Forum | Review | PDF | Favorites |
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