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):

$\lambda_J=\sqrt{\frac{\Phi_0}{2\pi\mu_0 d' j_c}},$

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

$d'=d_I %2B\lambda_1 \coth\left(\frac{d_1}{\lambda_1}\right) %2B\lambda_2 \coth\left(\frac{d_2}{\lambda_2}\right),$

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