Nonlocal Andreev transport through an interacting quantum dot

We investigate subgap transport through a single-level quantum dot tunnel coupled to one superconducting and two normal-conducting leads. Despite the tendency of a large charging energy to suppress the equilibrium proximity effect, a finite Andreev current through the dot can be achieved in nonequilibrium situations. We propose two schemes to identify nonlocal Andreev transport. In one of them, the presence of strong Coulomb interaction leads to negative values of the nonlocal conductance as a clear signal of nonlocal Andreev transport.

Figure 1

(Color online) Setup: a quantum dot is tunnel coupled to one superconducting and two normal-conducting leads. The latter may be ferromagnetic with magnetization directions ${\hat{\mathbf{m}}}_L$ and ${\hat{\mathbf{m}}}_R=\pm {\hat{\mathbf{m}}}_L$.

Figure 2

Andreev bound-state energies as a function of the level position $ϵ$, with ${\Gamma }_S/U=0.2$ and ${\Gamma }_N=0$.

Figure 3

TMR as a function of the polarization $p$ for different values of the detuning $\delta =2ϵ+U$. Inset: Current $J_S$ in the superconducting lead as a function of $ϵ$, for polarization $p=0.5$ and parallel and antiparallel alignments of the leads’ magnetization. For both graphs, we chose ${\mu }_L={\mu }_R={\mu }_N=U$, ${\mu }_S=0$, ${\Gamma }_S=0.2U$, ${\Gamma }_L={\Gamma }_R=0.001U$, and $k_{B}T=0.01U$.

Figure 4

(Color online) Current $J_R$ in the right lead as a function of the chemical potential ${\mu }_L$ of the left lead for different values of the detuning $\delta$ and ${\Gamma }_S=0.2U$, ${\Gamma }_L={\Gamma }_R=0.001U$, $p_L=p_R=0$, $k_{B}T=0.01U$, and (a) ${\mu }_R=0$ (small bias), (b) ${\mu }_R=0.5U$ (intermediate bias), and (c) ${\mu }_R=U$ (large bias).