Bound States for a Magnetic Impurity in a Superconductor

Abstract

We discuss a solvable model describing an Anderson like impurity in a BCS superconductor. The model can be mapped onto an Ising field theory in a boundary magnetic field, with the Ising fermions being the quasi-particles of the Bogoliubov transformation in BCS theory. The reflection S-matrix exhibits Andreev scattering, and the existence of bound states of the quasi-particles with the impurity lying inside the superconducting gap.