Size dependence in the disordered kondo problem

We study here the role randomly-placed non-magnetic scatterers play on the Kondo effect. We show that spin relaxation effects (with time tos)in the vertex corrections to the Kondo self-energy lead to an exact cancellation of the singular temperature dependence arising from the diffusion poles. For a thin film of thickness L and a mean-free path l, disorder provides a correction to the Kondo resistivity of the form Τ^o_s/(k_FLl²)lnT that explains both the disorder and sample-size depression of the Kondo effect observed by Blachly and Giordano [Phys. Rev. B 51, 12 537 (1995)].