London penetration depth

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In superconductivity, London penetration depth (usually denoted as $λ$ or $λ L$ ) characterizes the typical distance to which a weak magnetic field penetrates into a superconductor.

Typical values of $λ L$ are between 50 and 500nm. Deep inside a superconductor the magnetic field is zero (Meissner effect). For example, if one considers a superconducting semi-space at $x > 0$ , and weak external magnetic field $B 0$ applied along $z$ -direction in the empty space $x < 0$ , then inside the superconductor the magnetic field is given by

$B(x)=B_0\exp\left(-\frac{x}{\lambda_L}\right),$

i.e. $λ L$ is the distance across which magnetic field becomes $e$ times weaker. The above expression follows from the solution of the London equation with proper boundary conditions.