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

We study the time dependence of fluctuations of the order parameter in dirty type-II superconductors in the high-field region ($H\simeq H_{c2\mathrm{}}$). In this domain we can calculate their dispersion relation without taking into account the other collective modes (i.e., density and current oscillations), since the coupling of these oscillations with the order-parameter fluctuations is small (i.e., of the order of $\Delta$, which vanishes at $H=H_{c2\mathrm{}}$). Among many modes the following two are of special interest: the longitudinal mode, which couples to the density oscillations, and the transverse mode, which couples to the current oscillations. The longitudinal mode is of diffusion type at all temperatures. The transverse one is essentially damped, except in the vicinity of $T_{c0\mathrm{}}$ (critical temperature in zero field), where it is also diffusionlike. The thermal conductivity, ultrasonic attenuation, and spin susceptibility are not affected by the existence of these fluctuations. We calculate the transverse conductivity, which is strongly modified, showing an important anisotropy, which should be easily seen in surface-impedance measurements.