A Kondo hole is the charge neutral substitution of a rare earth ion by a non-magnetic analog. We consider the interaction between two Kondo holes in a Kondo insulator described by the non-degenerate Anderson lattice with a nearest-neighbor tight-binding conduction band on a simple cubic lattice. A Kondo hole introduces a bound state into the gap. The impurities form a strongly bound singlet if they are nearest neighbors. If they are further apart, they do not interact in the case of electron-hole symmetry. Without electron-hole symmetry non-nearest-neighbor impurities form a weakly bound spin singlet ground state, which can be overcome by moderate temperatures and/or high magnetic fields.
A Kondo hole is the charge neutral substitution of a rare earth (actinide) ion by a non-magnetic impurity, e.g. La (Th) replacing Ce (U). The addition of Kondo holes gradually destroys the coherence of the ground state of the Kondo insulator and introduces 6-function-like bound states in the hybridization gap. We previously reported on the local density of f-states (f-DOS) in the vicinity of an isolated Kondo hole [1,2], the formation of impurity bands for a finite concentration of Kondo holes [3,4], and the effects of doping and ligand defects [5].
In this paper, we extend our microscopic theory of the Kondo hole [1,2] to a pair of impurities to study possible interaction effects. For the isolated impurity the spectral weight of the bound state decreases rapidly with increasing distance from the impurity. Hence, we expect a pair of impurities to interact strongly only if they are nearest neighbors. The interaction arises from the interference in the scattering between the two impurities, which falls off rapidly with the distance between the impurities.
We consider the Anderson lattice, H 0, and the scattering potential due to the non-magnetic impurities at R~ and R2, Hi,