Kondo physics of magnetic adatoms on metallic surfaces when the onset of the surface conduction density of states crosses the Fermi level

We study the role of the onset of Shockley states, $D_s$, belonging to (111) surfaces of Cu, Ag and Au in the Kondo effect when a magnetic impurity is deposited on them. When $D_s$ approaches to the Fermi level, $E_F$, thing that can be done by compressing (stretching) the metallic sample, we found that most of the thermodynamic and dynamic properties of the impurity are affected in a non trivial way. We model the system by a generic Anderson impurity model and solve it by using the numerical renormalization group, NRG, technique. In particular, the impurity contribution to magnetic susceptibility and entropy as a function of temperature exhibit negative values and goes to zero slowly in a logarithmic shape. Furthermore, we found a suppression of the spectral density weight at the Fermi level when $D_s\sim E_F$ even in the Kondo regime. As a consequence, the conductance through the impurity is strongly reduced by near $25\mathrm{\%}$ of the unitary value $2e^2\mathrm{/}h$. Finally, we analyze these features in realistic systems like Co on Ag(111) reported in the literature.