RELAXATION AND COLLECTIVE MOTION IN SUPERCONDUCTORS - 2-FLUID DESCRIPTION

A simple, unified discussion of branch imbalance and gap relaxation in superconductors is presented. Both phenomena are treated within the framework of the ordinary Boltzmann equation, supplemented by the BCS gap equation. We show that the physics of the process commonly referred to as quasiparticle branch imbalance relaxation may be understood simply if one introduces a two-fluid model for the charge in the superconductor, and regards the process as one in which charge associated with the normal component is converted into charge associated with the superfluid. We derive in detail the exact solutions of the Boltzmann equation, which are valid near Tc, and allow for the effects of anisotropy. We discuss the comparison between relaxation rates measured in the superfluid and those obtained from normal state measurements and calculations. We then derive a set of two-fluid hydrodynamic equations based on the two-fluid model for the charge, and find that the current of charge associated with the normal component is not in general equal to the usual normal current. On the basis of these equations we derive expressions for the characteristic quasiparticle diffusion length near phase slip centers, and for the frequency of the recently observed collective mode. We compare our result with those of both microscopic and phenomenological calculations. © 1979.