Josephson penetration depth

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}{2pimu_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 +lambda_1 cothleft(frac{d_1}{lambda_1} ight) +lambda_2 cothleft(frac{d_2}{lambda_2} ight),

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.

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