Superconductor surface resistance If the superconductive state is due to a phase transition from ohmic to a state a zero-resistivity, why the superconductive materials are usually identified by their surface resistance, or by their RRR parameter?
 A: The problem of evaluation the surface resistance of a superconductor thin, is very important in the Superconductive Resonant Cavity in microwave band.
The response of a superconductor to RF fields as well described by the Two-Fluid Model that consist to identify the


*

*Cooper pairs as superfluid

*Unpaired electrons as normal fluid, yield conductivity $\sigma_n$.


Studying the response of two fluids to a periodic electric field we can separate the two different contributes:


*

*Normal Current by Ohm's Law $J_n=\sigma_nE_0\exp(-i\omega t)$

*Supercurrent given by London equations $J_s=i\frac{n_c 2 e^2}{m_e \omega}E_0 \exp(-i\omega t)$


Now we can write the total current as
$J=J_n+J_s = \sigma E_0 \exp(-i\omega t)$
with $\sigma$ is a complex conductivity given by
$\sigma = \sigma_n + i\sigma_s \text{ with } \sigma_s=\frac{2n_ce^2}{m_e\omega}=\frac{1}{\mu_0\lambda_L^2\omega}$
So, is possible to define the surface resistance as: the real part of the the complex surface impedance
$R_{surf} = \Re\left(\frac{1}{\lambda_L(\sigma_n+i\sigma_s)}\right)=\frac{1}{\lambda_L}\frac{\sigma_n}{\sigma_n^2+\sigma_s^2}$
at microwave frequency $\sigma_n^2 \ll \sigma_s^2 $ so $\boxed{R_{surf}\approx\frac{\sigma_n}{\lambda_L\sigma_s^2}}$
This model can be refined using an order parameter strictly link to the impurities of material.
Reference:
[1] - Basic Principles of RF Superconductivity and Superconducting
Cavities - Peter Schmuser
[2] - Surface Resistance of a Superconductor - H. Safa 
A: Superconductors possess zero resistance when cooled below critical temperature. There is a threshold between zero resistance and close-to-zero resistance.
I'm sending you links to two very useful links, you might want to check them out. Read this one and following Wikipedia article.
