The problem of a magnetic impurity, described by the Anderson impurity model, in a low carrier density system is considered. Such a system might be realized experimentally in strongly-doped semiconductors containing magnetic impurities. The simple cases of a one-hole impurity (e.g. Cu2+) or a one-electron impurity (like Ce3+) hybridizing with a nearly filled or nearly empty band are examined. It is shown that the physics of these systems is in various respects distinct from the Kondo effect of systems with partly-filled valence bands. Although the local susceptibility is strongly enhanced by the interactions, it is found at low doping ( delta ) a mass reduction of the quasiparticles at the Fermi energy (EF), if a (singlet) bound state is stable at zero doping. It is shown analytically that this is caused by band-edge effects. It is shown further that vastly different behaviour can be expected, depending on the filling of the impurity. For a one-electron impurity (Ce) interacting with an almost-filled valence band in the U= infinity limit, there is a one-particle-like bound state close to EF. As the doping is increased this state turns into a traditional Kondo resonance. In the case of a nearly filled impurity, however, the gap state is a two-particle singlet bound state, causing a singularity in the vertex function of the diagrammatic approach to the Kondo problem. In this limit the so-called noncrossing approximation breaks down. At intermediate doping levels it is no longer possible to identify a small parameter and for small and intermediate dopings we argue that the system is not characterized by a single energy scale.
 

Physical Review B, 46 15019-30, 1992.