Bound States for a Magnetic Impurity in a Superconductor

TL;DR

This paper presents a solvable model for a magnetic impurity in a superconductor, revealing bound states within the gap and connecting impurity effects to Ising field theory and Andreev scattering.

Contribution

It introduces a novel solvable model linking magnetic impurities in superconductors to Ising field theory, elucidating bound states and scattering phenomena.

Findings

Bound states exist inside the superconducting gap.

The model maps impurity effects to Ising boundary field theory.

Reflection S-matrix shows Andreev scattering behavior.

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.