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We know

"In the superconducting state, the DC electrical resistivity is zero."

But other situations has confused me a bit. There are several situations that superconductors interact with electromagnetic fields:

(1)Direct current electric field

(2)Alternative electric field

(3)Static magnetic field

(4)light

Under these situations, how to calculate the conductivity of superconductors? And which kinds of currents(current or Meissner current) contribute to conductivity? Which parts of superconductors(superfluid ground state part or quasi-particle excitation part) can contribute to conductivity?

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"Conductivity" in reference to an actual superconductor doesn't really make sense.

Conductivity is in relation to materials that obey forms of ohms law, and is a proportionality constant between an applied electric field and current density.

The commonly prescribed Conductivity for superconductors is $\infty$, but that still doesn't make sense since that would mean the current is infinity for any electric field. Current in a superconductor should be modelled as free electrons, or:

$$\frac{d\vec{J}}{dt}=\frac{e^2n}{m} \vec{E}$$

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