Role of the surface state in the Kondo resonance width of a Co single adatom on Ag(111)

We address the long-term controversy on the fundamental question of the role of the surface state on the Kondo effect with Co adatoms on a Ag(111) surface. The width of the Kondo resonance oscillates with the same period of half Fermi wavelength of the surface state. But the amplitude increases for a Co adatom placed next to another Co adatom, at the vicinity of a step edge, and quantum confined within nanocorrals. A greater than three times enhancement of the resonance width can be achieved when quantum confinement is introduced. The experimental results are described quantitatively utilizing an analytical model where the contributions of the bulk and surface states are weighted by their exchange values with the magnetic impurity. These findings clarify the role of the surface state on the Kondo effect and pave a pathway to tailor the Kondo effect via quantum confinement of the surface state.