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 $H_{c2\mathrm{}}$, where the equilibrium value of the order parameter $\Delta \left(\mathbf{r}\right)$ 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 $D\cong {\xi }_0{v}^2$, where ${\xi }_0$ is the coherence distance and $v$ the Fermi velocity. (2) The transverse mode, which couples to the current fluctuations. At high temperature (i.e., $T\sim T_{c0\mathrm{}}$, where $T_{c0\mathrm{}}$ 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., $\omega <T_{c0\mathrm{}}$). This modifies strongly both the surface impedance and the attenuation coefficient of a transverse ultrasonic wave in the corresponding geometry.