Microwave Surface Impedance of Superconductors of the Second Kind

A simplified model of the mixed state of a superconductor of the second kind is proposed. The generation and parallel alignment of "fluxo\"{}ds" under the influence of an externally applied magnetic field results in a medium whose conductivity is position-dependent in all directions perpendicular to the applied field. The proposed model is that of a two-fluid superconductor with carrier concentrations sinuso\"{}dally space-modulated in only one direction. This model is found to account extremely well for the experimentally observed behavior. In particular, the large dependence of the absorption of energy on the relative angle between applied dc field and induced microwave current is satisfactorily explained. The ratio of absorbed energies in the perpendicular and parallel configurations is predicted to lie between 1 and 7, whereas recent experiments with various materials have yielded ratios between 1 and 15. Our model also predicts that this anisotropy is not very dependent on temperature and applied magnetic field, also in agreement with experimental findings.