Impurity bands in Kondo insulators

Kondo insulators like ${\mathrm{Ce}}_3$ ${\mathrm{Bi}}_4$ ${\mathrm{Pt}}_3$ and CeNiSn are compounds with small-band-gap semiconductor properties. Nonmagnetic impurities, so-called Kondo holes, break the translational invariance and hence the coherence of the ground state. Isolated impurities give rise to a bound state in the gap, which pins the Fermi level and has magnetic properties (Curie susceptibility and Schottky anomaly in the specific heat). A finite concentration of Kondo holes gives rise to an impurity band inside the gap of the f-electron density of states, whose height and width are proportional to √c for small concentrations. The specific heat is proportional to T at very low temperatures and the susceptibility is Pauli-like at low T. The correlations within the f band are introduced via a self-energy, evaluated to second-order perturbation in U. We use the (1/d)-expansion method of Schweitzer and Czycholl to leading order in which the k integrations are properly carried out, but the k dependence of the self-energy is neglected. The main effect of U is to narrow the gap, as well as the impurity band.