Size Dependence in the Disordered Kondo Problem

We study here the role randomly placed nonmagnetic scatterers play on the Kondo effect. We show that spin-relaxation effects (with time ${\tau }_s^0$) 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 $\ell$, disorder provides a correction to the Kondo resistivity of the form ${\tau }_s^0/\left(k_{F}L{\ell }^2\right)\ln T$ that explains the disorder-induced depression of the Kondo effect observed by Blachly and Giordano [Phys. Rev. B 51, 12 537 (1995)].