London penetration depth

In superconductors, the London penetration depth (usually denoted as ${\displaystyle \lambda }$ or ${\displaystyle \lambda _{L}}$) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to ${\displaystyle e}$⁻¹ times that of the magnetic field at the surface of the superconductor. Typical values of λ_L range from 50 to 500 nm.

The London penetration depth results from considering the London equation and Ampère's circuital law. If one considers a superconducting half-space, i.e superconducting for x>0, and weak external magnetic field B₀ applied along z direction in the empty space x<0, then inside the superconductor the magnetic field is given by

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