Anderson impurity in a semiconductor

TL;DR

This paper investigates the behavior of an Anderson impurity model with a gapped host, revealing that particle-hole symmetry leads to non-Fermi liquid behavior, while asymmetry results in a generalized Fermi liquid, supported by perturbative analysis and NRG comparisons.

Contribution

It provides a perturbative analysis of the Anderson impurity in a gapped host, distinguishing Fermi liquid and non-Fermi liquid regimes based on particle-hole symmetry.

Findings

Particle-hole asymmetry yields a generalized Fermi liquid.

Particle-hole symmetric point is a non-Fermi liquid.

Results agree with numerical renormalization group studies.

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 non-interacting 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 non-interacting limit, and as such is a non-Fermi liquid for all non-zero gaps. Our conclusions are in agreement with NRG studies of the problem.