Anisotropy of the Surface Impedance in the Surface-Sheath Regime as Evidence for Fluctuations of the Superconducting Order Parameter

In the surface-sheath regime, the high-frequency surface impedance of a superconductor is a function of the angle between the polarization plane of the incident wave's electric vector ${\mathbf{E}}_{\omega }$ and the steady magnetic field H. This anisotropy arises from collective fluctuations of the superconducting order parameter $\Delta \mathrm{}\left(x\right)\mathrm{}$. In the ground state $\Delta \mathrm{}\left(x\right)\mathrm{}$ is a modeless function. When ${\mathbf{E}}_{\omega }$ and H are perpendicular, the incident electromagnetic wave can couple to the intrinsic sheath currents and excite $\Delta \mathrm{}\left(x\right)\mathrm{}$ into states with a finite damping coefficient. No such excitations are possible when ${\mathbf{E}}_{\omega }$ and H are parallel. The extra absorption predicted by theory in the dirty limit explains experimental data obtained from two lead-based alloys very well. These experiments should, therefore, be considered as direct evidence for the existence of collective fluctuations of the order parameter in the surface-sheath regime of superconductors.