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

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

where d_I is the thickness of the Josephson barrier (usually insulator), d_1,2 are the thicknesses of superconducting electrodes, and λ_1,2 are their London penetration depths.