Fluctuations of the Order Parameter in Type-II Superconductors. II. Pure Limit

We study here the fluctuations of the order parameter in pure type-II superconductors in the vicinity of the upper critical field Hc2, where the equilibrium value of the order parameter Δ(r) is described in terms of the Abrikosov solution. Among many fluctuations we concentrate on two modes: (1) The longitudinal mode, which couples to the density fluctuations. This mode is described by an equation of diffusion type at all temperatures. The diffusion coefficient is weakly temperature-dependent and given by Dξ₀v², where ξ₀ is the coherence distance and v the Fermi velocity. (2) The transverse mode, which couples to the current fluctuations. At high temperature (i.e., T~Tc0, where Tc0 is the critical temperature in zero field) this mode is of diffusion type, while at low temperature, it becomes a strongly damped oscillation. We show that the transverse modes cause an important modification of the electromagnetic response of the type-II superconductor. When the oscillating current flows in the plane perpendicular to the static magnetic field, the reactive part of the resulting response vanishes identically at low frequency (i.e., ω<Tc0). This modifies strongly both the surface impedance and the attenuation coefficient of a transverse ultrasonic wave in the corresponding geometry.