Transport properties of a two-impurity system: A theoretical approach

A system of two interacting cobalt atoms, at varying distances, was studied in a recent scanning tunneling microscope experiment by Bork et al. [Nat. Phys. 7, 901 (2011)]. We propose a microscopic model that explains, for all experimentally analyzed interatomic distances, the physics observed in these experiments. Our proposal is based on the two-impurity Anderson model, with the inclusion of a two-path geometry for charge transport. This many-body system is treated in the finite-$U$ slave boson mean-field approximation and the logarithmic-discretization embedded-cluster approximation. We physically characterize the different charge transport regimes of this system at various interatomic distances and show that, as in the experiments, the features observed in the transport properties depend on the presence of two impurities but also on the existence of two conducting channels for electron transport. We interpret the splitting observed in the conductance as the result of the hybridization of the two Kondo resonances associated with each impurity.

Figure 1

Schematic of the model studied in this work. $\alpha$ and $\beta$ represent the two Co atoms.

Figure 2

Differential conductance as a function of $V/T_K^0$ for $300\le z\le -60$ [where $z$ is the separation between the impurities (in pm), indicated at the right]. Each curve, calculated using SBMFA, has been shifted vertically for clarity.

Figure 3

Conductance $G/G_0$ as a function of $z$. Compared to Fig. 4(a) in Ref. 23, we see the same overall behavior. Inset: Renormalized energy level ${\tilde{\epsilon }}_{\alpha }={\tilde{\epsilon }}_{\beta }=\tilde{\epsilon }$ as a function of gate voltage $V_g$. The plateau at the Fermi energy for both $z=200$ [solid (black) line] and $z=-60$ [diamond (red) line] indicates that the system stays in the Kondo regime. For larger hopping values, $t_{\alpha \beta }=0.06$ and $t_{LR}=0.13$, the plateau starts to be suppressed, as shown by the dashed (green) curve for $z=-150$, reflecting that the system enters a crossover regime (see text).

Figure 4

Splitting as a function of $z$ [solid (black) curve]. Lower inset: Width of the antiresonance, as a function of distance, in units of $T_K^0$. The SBMFA results (black line) are similar to those obtained in Figs. 5(b) and 5(a) in Ref. 23 [reproduced schematically here as filled (red) circles]. Upper inset: Spin-spin correlations between the impurities [solid (black) curve] and between each impurity and its adjacent reservoir [dashed (green) curve; see text].

Figure 5

Differential conductance for a single impurity as a function of $V/T_K^0$. The behavior is markedly different from the case of two atoms, as in the experiments.