Tuning The Kondo Effect With The Surface State:Experimental And Theoretical Studies

The Kondo effect is one of the most studied electron correlation phenomena in condensed matter physics.It describes the spin of magnetic impurity in nonmagnetic host interacting with the spins of surrounding conduction electrons.At low temperature,a many-body nonmagnetic singlet ground state is formed,resulting a spectroscopic signature around the Fermi level of the host,i.e.the Kondo or Abrikosov-Suhl resonance.To date,the resonance can be investigated down to a single atom or single molecular level with low temperature scanning tunneling spectroscopy(STS).There is a characteristic temperature called Kondo temperature(Tk)and it is associated with the density of states(DOS)at Fermi level ?(EF)and the exchange constant J.When a surface state crosses the Fermi level,it is thus anticipated to influence TK.However,the fundamental questions on whether and how the surface state influences TK remain as an ongoing debate.By using atomic manipulation with LT-STM,we performed systematic studies of the Kondo resonance for Co monomers on Ag(111)and found compelling evidence that the surface state does influence the Kondo temperature.Kondo temperature oscillations with increasing amplitude are found for the three cases studied of a Co adatom(i)placed next to another Co adatom,(ii)at the vicinity of a step edge,and(iii)quantum confined within nanocorrals.Our findings can be understood by an analytical model where the contributions of surface and bulk states are weighted by their exchange values with the Co adatom,Jb and Js.Within the model,Jb and JS are derived consistently for all three cases.Our findings also demonstrate an approach to control the Kondo effect via the local modification of the LDOS of the surface state.In comparing with previous methods,our approach has the advantage that the Kondo effect can be continuously tuned with large magnitude,thus providing new opportunities in spintronics and spin-based quantum information processing.Our experimental observation showed that Kondo temperature of Co adatoms placed at the center of nano-corrals on the surface of Ag(111)oscillates strongly as a function of the diameter of the corral built by multi-adatoms.The understanding of the effect demands a theory to describe the Kondo effect in the condition that multi-adatoms are involved.In order to address the complicated situation where multiple magnetic impurities are adsorbed on the surface of noble metals,we construct a theory based on the duality between strong and weak coupling limit in Anderson impurity model.The multiple impurities on the surface are discussed by considering the renormalization effect due to the inter-adatom couplings.Our calculations not only reproduces the recent experimental finding of the oscillations of the Kondo resonance width(the half width of the half maximum of the Kondo resonance peak)versus the quantum corral size but also predicts that it should also oscillate as a function of the separation from the quantum corral center.We further performed the low-temperature STS measurements and found one to one correspondence with the prediction.The good agreement between the theory and experiments demonstrates the validity of our approach to the Kondo problems with the involvement of multi-adatoms.