Nonlocal electrodynamics of superconductors

[physengineer]

Hello,

Conductivity $\sigma (\omega, k)$ in Fourier space is defined by

$$J(\omega, k)= \sigma (\omega, k) A(\omega, k)$$

In most cases the local limit of $k\rightarrow 0$ is a good approximation particulalry in type I superconductors and HTC superconductors.

I am interested in cases where non-local electrodynamics $k\neq 0$ is important. I would appreciate it if you could help me with

1-Can this nonlocality be observed?
2- Are there any applications based on this nonlocality?
3- Are you aware of any experiments or theoretical works that emphasises or uses this?
4-Anything related to the importance of nonlocal elecytrodynamics?

Thanks a lot in advance!

 

[DrDu]

Take in mind that the relation between J and the electric or magnetic fields is very non-local even if the k dependence of sigma were negligible due to the very non local dependence of A on B.
The k dependence of sigma is observed in superconductors of Pippard type, e.g. in the skin effect.