It is well known that many materials, known as superconductors, lose all DC electrical resistance when the temperature drops below the critical temperature Tc . The BCS theory has quite successfully described this phenomenon. According to BCS theory, below Tc the electrons of a conductor gain a small net attraction through their interaction with the surrounding lattice. The Cooper pairs have binding energy Delta, which is dependent on temperature. At temperatures above absolute zero, but below the critical temperature, the surface resistance is greatly reduced, yet non-zero.
Cooper pairs move without resistance, and thus dissipate no power.
The Cooper pairs do nonetheless have an inertial mass, and thus the electromagnetic fields must extend into the surface of the conductor in order to provide the forces to accelerate the pairs back and forth to sustain the RF surface currents. The EM fields will act on the unpaired electrons as well, therefore causing power dissipation. The coefficient A is a complex function of material parameters such as the superconducting coherence length, the penetration depth, the electron mean free path, and the Fermi velocity. The second term on the right hand side of equation 8 is the residual, or temperature independent, resistance R0 . Mechanisms for R0 are not well understood, though several possiblilities have been proposed and investigated.