Josephson penetration depth

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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 λJ and is given by the following expression (in SI):

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

where Φ0 is the magnetic flux quantum, jc is the critical current density (A / cm2), and d' characterizes the inductance of the superconducting electrodes

d'=d_I +\lambda_1 \coth\left(\frac{d_1}{\lambda_1}\right) +\lambda_2 \coth\left(\frac{d_2}{\lambda_2}\right),

where dI is the thickness of the Josephson barrier (usually insulator), d1,2 are the thicknesses of superconducting electrodes, and λ1,2 are their London penetration depths.