Spatial variations of the order parameter in superconductors containing a magnetic impurity

The spatial variation of the superconductor order parameter in the presence of a classical spin has been analyzed by solving self-consistently the Gorkov equation for the one-particle Green's function. In the vicinity of the impurity the deviations from the bulk pair potential $\Delta$ is of the form $\frac{\Delta A\left(T\right)\mathrm{}{sin}^2{k}_{F}r}{{\left(k_{F}r\right)}^2}$, where $A\left(T\right)\mathrm{}$ is a temperature-dependent factor. At large distances from the impurity, $r\gg {\xi }_0$ (${\xi }_0$ is the superconductor coherence length at zero temperature), $\Delta \mathrm{}\left(r\right)\mathrm{}$ varies like $\frac{1}{r}$ near the transition temperature, as is expected from the Ginzburg-Landau theory. At low temperatures the spatial dependence is oscillatory and decreases as $\frac{1}{r^3}$.