What do we know of superconductivity in thin layers?

motivated by another question, i wonder if there are special properties of superconductivity when restricted on 2D or very thin layers related to the effective permittivity in function of the frequency $\epsilon ( \omega )$ near the first-order transitions between the superconducting and normal phases , any references about the main state of the art would be appreciated

Edit: I've noticed that most research papers on superconductivity report on the current transport properties, but they usually don't talk much about the permittivity. Is this because its harder to measure?

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When the magnetic field is such that the system lies on the "plateaus", in between the quantized resistance values, the 2DEG in the bulk of the sample is in a superconductivity state exhibiting dissipationless transport. This is also depicted by the green line in the plot which measures the longitudinal resistance $\rho_{xx}$ of the sample. We see that this quantity vanishes precisely when the system is on a plateau indicating the presence of superflow in the longitudinal direction.
-1. This is incredibly wrong -- there is no superflow in QHE! Superconductivity is much more than vanishing $\rho_{xx}$ anyway, and it is also trivially seen that the dc conductivity $\sigma_{xx} = 0$ in quantum Hall systems as well (this is because resistivity is the inverse of the conductivity tensor). –  wsc Mar 11 '11 at 21:42