Interplay between quantum interference and Kondo effects in nonequilibrium transport through nanoscopic systems

We calculate the finite temperature and nonequilibrium electric current through systems described generically at low energy by a singlet and two spin doublets for $N$ and $N\pm 1$ electrons, respectively, coupled asymmetrically to two conducting leads, which allows for destructive interference in the conductance. The model is suitable for studying transport in a great variety of systems such as aromatic molecules, different geometries of quantum dots, and rings with applied magnetic flux. As a consequence of the interplay between interference and Kondo effect, we find changes by several orders of magnitude in the values of the conductance and its temperature dependence as the doublet level splitting is changed by some external parameter. The differential conductance at finite bias is negative for some parameters.

Figure 1

Scheme of the relevant matrix elements at low energies.

Figure 2

Equilibrium conductance and $T\ll T_K$ (left scale) and occupation numbers (right scale) as a function of the level splitting. Squares were obtained by numerical differentiation of the current and circles correspond to Eq. (2). Inset: Kondo temperature as a function of $\delta$. Squares (solid line) correspond to the NCA (analytical) result. Parameters are $\Delta =0.5$, $D=10$, $E_1=-4$, and $E_2=E_1+\delta$.

Figure 3

Equilibrium conductance as a function of temperature for several level splittings. Dashed [dashed-dot] line corresponds to the limit of one-level SU(4) [SU(2)] Anderson model. Other parameters as in Fig. 2. For $\delta =0.0035$, $G_0=0.08$ and $T_K^{*}=0.0137$, while for $\delta =0.06$, $G_0=0.97$ and $T_K^{*}=0.0025$.

Figure 4

Differential conductance as a function of bias voltage at different temperatures for $\delta =0.0112$. Other parameters as in Fig. 2.

Figure 5

Current as a function of level splitting $\delta$ for $eV=T_K^4=0.016$ and different temperatures proportional to $T_K\left(\delta \right)$. Other parameters as in Fig. 2.