Impure Kondo insulators

A Kondo hole is the charge neutral substitution of a rare earth ion by a nonmagnetic analog. We consider an arbitrary cluster of Kondo holes in a Kondo insulator described by the nondegenerate symmetric Anderson lattice with a nearest-neighbor tight-binding conduction band on a simple cubic lattice. Each Kondo hole introduces a bound state in the gap. Quantum interference in the scattering off the impurities gives rise to interactions among the Kondo holes. The interaction is strong if the impurities are nearest neighbors, but weak if they are further apart. The wave function of the bound states is predominantly localized on the sites neighboring the Kondo holes. Clusters of impurities separated by more than two hoppings are disconnected for bound states at the Fermi level, i.e. the wave functions do not overlap. The possibility of a metal-insulator transition can then be reduced to a site percolation of Kondo holes.