The two-fluid model of superconductivity

Abstract

The basis of the two-fluid model of superconductivity is discussed especially for dirty superconductors. It is shown that for the free-electron model of a metal the superfluid velocity can be defined by vs = ps/m where the macroscopic order parameter depends on position through the phase factor ps · r, and where m is the band mass. With this definition of vs the energy and current densities have the same form in pure and impure materials. It is shown further that, for consistency with the conservation of energy, the time development of vs is given by the usual macroscopic equation even in very impure material.