# Josephson penetration depth

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Josephson penetration depth

In superconductivity, Josephson penetration depth characterizes the typical length on which an externally-applied magnetic field penetrates into the long Josephson junction. Josephson penetration depth is usually denoted as $lambda_J$ and is given by the following expression (in SI):

$lambda_J=sqrt\left\{frac\left\{Phi_0\right\}\left\{2pimu_0 d\text{'} j_c,$

where $Phi_0$ is the magnetic flux quantum, $j_c$ is the critical current density $mathrm\left\{\left(A/cm^2\right)\right\}$, and $d\text{'}$ characterizes the inductance of the superconducting electrodes

$d\text{'}=d_I +lambda_1 cothleft\left(frac\left\{d_1\right\}\left\{lambda_1\right\} ight\right) +lambda_2 cothleft\left(frac\left\{d_2\right\}\left\{lambda_2\right\} ight\right),$

where $d_I$ is the thickness of the Josephson barrier (usually insulator), $d_\left\{1,2\right\}$ are the thicknesses of superconducting electrodes, and $lambda_\left\{1,2\right\}$ are their London penetration depths.

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