Local properties of a superconductor in the presence of a magnetic impurity

The physics of magnetic impurities in superconducting hosts has long been a subject of theoretical and experimental inquiry. Most theoretical work (14, 52, 53) has focussed on bulk properties, such as the transition temperature and density of states, which can be calculated using the impurity averaging technique. This thesis is devoted to the detailed study of the local properties of a superconductor in the presence of a single such impurity. We develop a general theory for the local environment of a magnetic impurity in a superconductor, using an Anderson Model to describe the impurity. We can thus cover many regimes (i.e. Kondo, mixed valence) of physical interest. We studied the spatial dependence of the order parameter in the two regimes. In the Kondo limit, the spin correlation function between the impurity spin and the conduction spins, and the local density of states near the impurity are studied. In this problem there are two characteristic length scales, the superconducting coherence length, and the Kondo length. The interplay between these two length scales leads to rich spatial structure, which is manifested through various local properties studied here