Three-terminal transport through a quantum dot in the Kondo regime: Conductance, dephasing, and current-current correlations

We investigate the nonequilibrium transport properties of a three-terminal quantum dot in the strongly interacting limit. At low temperatures, a Kondo resonance arises from the antiferromagnetic coupling between the localized electron in the quantum dot and the conduction electrons in source and drain leads. It is known that the local density of states is accessible through the differential conductance measured at the (weakly coupled) third lead. Here, we consider the multiterminal current-current correlations (shot noise and cross correlations measured at two different terminals). We discuss the dependence of the current correlations on a number of external parameters: bias voltage, magnetic field, and magnetization of the leads. When the Kondo resonance is split by fixing the voltage bias between two leads, the shot noise shows a nontrivial dependence on the voltage applied to the third lead. We show that the cross correlations of the current are more sensitive than the conductance to the appearance of an external magnetic field. When the leads are ferromagnetic and their magnetizations point along opposite directions, we find a reduction of the cross correlations. Moreover, we report on the effect of dephasing in the Kondo state for a two-terminal geometry when the third lead plays the role of a fictitious voltage probe.

Figure 1

The system under consideration. The central island is a resonant level coupled to three leads. The level may be shifted through a capacitative coupling to a gate. In the limit of a vanishingly small capacitance, double occupancy in the dot is forbidden and Kondo effect can arise. The current-current cross correlations are measured between leads 2 and 3.

Figure 2

(a) Differential conductance $G_{11}$ vs bias voltage $V_1$ as a function of the bare coupling ${\Gamma }_3$ to the voltage probe (reservoir 3) for ${\Gamma }_1={\Gamma }_2$ and ${\epsilon }_0=-6\Gamma$. (b) Linear conductance $G_{11}\left(0\right)$ showing the reduction of the peak in (a) vs the coupling to the voltage probe. The dots are numerical results where the line corresponds to an analytical formula (see text).

Figure 3

(a) Differential conductance $G_{11}$ vs bias voltage $V_1$ for ${\epsilon }_0=-6\Gamma$ $(T_K^0=8\times {10}^{-3}\Gamma )$. (b) Dependence of the Kondo temperature on $V_1$.

Figure 4

(a) Current-current cross correlation measured in leads 2 and 3, $S_{23}\left(0\right)$, as a function of the bias voltage in the injecting lead $V_1$. Kondo correlations involve an increase of $S_{23}\left(0\right)$ for voltages larger than $2T_K$. (b) Same as (a) for a noninteracting quantum dot with a resonant level exactly at $E_F$. (c) and (d) correspond to the Fano factor ${\gamma }_{23}$ as a function of voltage for the interacting and noninteracting case respectively.

Figure 5

Differential conductance $G_{11}$ vs bias voltage $V_1$ for different values of the voltage difference $\Delta V\equiv \mid V_2-V_3\mid \gtrsim 2T_K^0$.

Figure 6

(a) Cross correlations of the current measured between leads 2 and 3 for the case treated in Fig. 5. (b) Same as (a) for the shot noise in lead 1.

Figure 7

(a) Differential conductance $G_{11}$ vs $V_{11}$ as a function of the Zeeman term ${\Delta }_Z$ for $V_2=V_3=0$. (b) Same as (a) for the Fano factor of the cross correlator ${\gamma }_{23}$.

Figure 8

Fano factor of the cross correlator, ${\gamma }_{23}$ vs $V_1∕T_K^0$ for different lead magnetization when $V_2=V_3=0$. (a) Parallel alignment between the magnetizations of the leads with spin polarizations: $p_1=p_2=p_3=p$. (b) Antiparallel case with $p_1=-p_2=-p_3=p$.