Electronic structure of a conventional superconductor in the vicinity of a single, iso- lated magnetic impurity has been probed experimentally with scanning tunneling spectroscopy by Yazdani et al.. Motivated by their experiment, we study the ef- fects of a single magnetic impurity on superconductivity by means of the mean-¯eld Bogoliubov-de Gennes theory. The Bogoliubov-de Gennes equations are solved di- rectly and numerically, utilizing parallel computation on a CFI-founded 128-CPU Beowulf-class PC cluster here at the University of Saskatchewan. As a preliminary study, we also examine the electronic structure around a magnetic vortex. The local magnetic field around a vortex breaks up Cooper pairs and suppresses superconduc- tivity locally. Quasiparticle excitations are created and bound in the vortex core area due to repeated Andreev scattering. A magnetic impurity tends to align the spins of the neighboring electrons and break up Cooper pairs, and has similar effects of lo- cally suppressing superconductivity. A striking difference, however, from the vortex problem is that around a magnetic impurity there is particle-hole asymmetry in the tunneling conductance. This is due to different probability amplitudes in the spin-up branch and the spin-down branch of quasiparticle excitations. Furthermore, for the spin potential strength larger than a certain critical value, the nature of quasiparticle excitations is changed dramatically. Within a model of classical spin, we propose an explanation of the measured tunneling conductance of the experiment. This work is significant in that it gives us insight into superconductivity and magnetism{two complementary manifestation of strong electron correlations.

Electronic structure of a conventional superconductor in the vicinity of a single, iso- lated magnetic impurity has been probed experimentally with scanning tunneling spectroscopy by Yazdani et al.. Motivated by their experiment, we study the ef- fects of a single magnetic impurity on superconductivity by means of the mean-¯eld Bogoliubov-de Gennes theory. The Bogoliubov-de Gennes equations are solved di- rectly and numerically, utilizing parallel computation on a CFI-founded 128-CPU Beowulf-class PC cluster here at the University of Saskatchewan. As a preliminary study, we also examine the electronic structure around a magnetic vortex. The local magnetic field around a vortex breaks up Cooper pairs and suppresses superconduc- tivity locally. Quasiparticle excitations are created and bound in the vortex core area due to repeated Andreev scattering. A magnetic impurity tends to align the spins of the neighboring electrons and break up Cooper pairs, and has similar effects of lo- cally suppressing superconductivity. A striking difference, however, from the vortex problem is that around a magnetic impurity there is particle-hole asymmetry in the tunneling conductance. This is due to different probability amplitudes in the spin-up branch and the spin-down branch of quasiparticle excitations. Furthermore, for the spin potential strength larger than a certain critical value, the nature of quasiparticle excitations is changed dramatically. Within a model of classical spin, we propose an explanation of the measured tunneling conductance of the experiment. This work is significant in that it gives us insight into superconductivity and magnetism{two complementary manifestation of strong electron correlations.