Relevance of the complete Coulomb interaction matrix for the Kondo problem: Co impurities in Cu hosts

The electronic structure of a prototype Kondo system, a cobalt impurity in a copper host is calculated, accurately taking into account correlation effects on the Co atom. Using the recently developed continuous-time Quantum Monte Carlo technique, it is possible to describe the Kondo resonance with a complete four-index Coulomb interaction matrix. We demonstrate that a standard practice of using a truncated Hubbard Hamiltonian to consider the Kondo physics can be inadequate. Using the full Coulomb vertex on Co, we study the qualitative dependence of the Kondo resonance on the local coordination.

Figure 1

(Color online) Comparison with ED in the atomic limit (without hybridization to the bath of free electrons). Main graph: $U=1\text{eV}$, $J=0.4\text{eV}$ and $\beta =2{\text{eV}}^{-1}$, for five-orbital impurity at half filling; inset: $U=2\text{eV}$, $J=0.7\text{eV}$, and $\beta =3.7{\text{eV}}^{-1}$, for five-orbital impurity with eight electrons.

Figure 2

(Color online) Histograms of Monte Carlo distributions for average perturbation order. Main graph: $U=4\text{eV}$, $J=0.7\text{eV}$, and $\beta =10{\text{eV}}^{-1}$ for five-orbital impurity coupled to realistic Cu bath with seven electrons; inset: $U=4\text{eV}$, $J=0.7\text{eV}$, and $\beta =1{\text{eV}}^{-1}$ in the case of five-orbital impurity model, coupled to semielliptical bath with bandwidth $W=0.5\text{eV}$ at the half filling.

Figure 3

(Color online) Total DOS of $3d$ orbital of Co atom embedded in Cu matrix. Model parameters: $U=4\text{eV}$, $J=0.7\text{eV}$, and $\beta =10{\text{eV}}^{-1}$ for five-orbital impurity with seven electrons.

Figure 4

(Color online)Total DOS of $3d$ orbital of Co atom embedded in the bulk of Cu, into first layer and Co adatom on the Cu(111) surface. Model parameters: $U=4\text{eV}$, $J=0.7\text{eV}$, and $\beta =10{\text{eV}}^{-1}$ for five-orbital impurity with seven electrons.