Co adatoms on Cu surfaces: Ballistic conductance and Kondo temperature

Abstract

The Kondo zero-bias anomaly of Co adatoms probed by scanning tunneling microscopy is known to depend on the height of the tip above the surface, and this dependence is different on different low index Cu surfaces. On the (100) surface, the Kondo temperature first decreases then increases as the tip approaches the adatom, while on the (111) surface it is virtually unaffected. These trends are captured by combined density functional theory and numerical renormalization-group calculations. The adatoms are found to be described by an $S=1$ Anderson model on both surfaces, and ab initio calculations help identify the symmetry of the active $d$ orbitals. We correctly reproduce the Fano line shape of the zero-bias anomaly for Co/Cu(100) in the tunneling regime but not in the contact regime, where it is probably dependent on the details of the tip and contact geometry. The line shape for Co/Cu(111) is presumably affected by the presence of surface states, which are not included in our method. We also discuss the role of symmetry, which is preserved in our model scattering geometry but most likely broken in experimental conditions.