I Is London depth in superconductors analogous to skin depth?

[iVenky]

London penetration depth that's defined for superconductors has a similar equation to skin depth in conductors derived from maxwell's equations. Are they equivalent?

 

[vanhees71]

Physically they are not too much equivalent, because the skin depth is due to a dissipation effect, i.e., the finite electric conductivity while the London penetration depth is related to the effective photon mass within a superconductor due to the Anderson-Higgs mechanism.

https://en.wikipedia.org/wiki/Skin_effect
https://en.wikipedia.org/wiki/Ginzburg–Landau_theory

 

[f95toli]

Yes, from a practical point of view they are somewhat similar.
However, there are not "the same thing"; you can for example not replace the skin depth by the penetration depth when e.g. calculating EM properties.
The EM properties of superconductors at low frequencies (frequencies much lower than the energy of the gap) behave pretty much like perfect conductors from a EM point of view. The main difference (for type II superconductors) is actually presence of a fairly significant kinetic inductance, rather than the penetration depth.