Anderson impurity model in a semiconductor

Abstract

We consider an Anderson impurity model in which the locally correlated orbital is coupled to a host with a gapped density of states. Single-particle dynamics are studied within a perturbative framework that includes both explicit second-order perturbation theory and self-consistent perturbation theory to all orders in the interaction. Away from particle-hole symmetry, the system is shown to be a generalized Fermi liquid (GFL) in the sense of being perturbatively connectable to the noninteracting limit, and the exact Friedel sum rule for the GFL phase is obtained. We show by contrast that the particle-hole-symmetric point of the model is not perturbatively connected to the noninteracting limit and as such is a non-Fermi liquid for all nonzero gaps. Our conclusions are in agreement with numerical renormalization group studies of the problem.