Kondo temperature when the Fermi level is near a step in the conduction density of states

The (111) surface of Cu, Ag, and Au is characterized by a band of surface Shockley states with a constant density of states beginning slightly below the Fermi energy. These states as well as bulk states hybridize with magnetic impurities which can be placed above the surface. We calculate the characteristic low-temperature energy scale, the Kondo temperature ${T}_K$ of the impurity Anderson model, as the bottom of the conduction band ${D}_s$ crosses the Fermi energy ${\ensuremath{\epsilon}}_F$. We find simple power laws ${T}_K\ensuremath{\simeq}{|{D}_s\ensuremath{-}{\ensuremath{\epsilon}}_F|}^{\ensuremath{\eta}}$, where $\ensuremath{\eta}$ depends on the sign of ${D}_s\ensuremath{-}{\ensuremath{\epsilon}}_F$, the ratio between surface and bulk hybridizations with the impurity ${\mathrm{\ensuremath{\Delta}}}_s/{\mathrm{\ensuremath{\Delta}}}_b$, and the ratio between on-site and Coulomb energy ${E}_d/U$ in the model.