Superconducting proximity effect in interacting double-dot systems

We study subgap transport from a superconductor through a double quantum dot with large on-site Coulomb repulsion to two normal leads. Nonlocal superconducting correlations in the double dot are induced by the proximity to the superconducting lead, detectable in nonlocal Andreev transport that splits Cooper pairs in locally separated, spin-entangled electrons. We find that the $I\text{−}V$ characteristics are strongly asymmetric: for a large bias voltage of certain polarity, transport is blocked by populating the double dot with states whose spin symmetry is incompatible with the superconductor. Furthermore, by tuning gate voltages one has access to splitting of the Andreev excitation energies, which is visible in the differential conductance.

Figure 1

(Color online) Schematic setup of a double quantum dot, tunnel coupled to two normal and one superconducting leads. The double-dot system can be driven out of equilibrium by applying a finite bias voltages to the normal leads.

Figure 2

(Color online) Density plot of the current injected into the superconducting lead $I_S$ in units of $\left(e{\Gamma }_N\right)/\hslash$ as a function of the detuning $\delta ={\epsilon }_L+{\epsilon }_R+U$ and of the chemical potential $\mu$ of the normal leads for degenerate dots’ levels $\Delta \epsilon =0$. The other parameters are: ${\Gamma }_S=0.5U$ and $k_{B}T=0.01U$.

Figure 3

(Color online) Density plot of the differential conductance in units of $G_{\text{tunn}}=\left(e^2/h\right){\Gamma }_N/\left(2\pi k_{B}T\right)$ as a function of the detuning $\delta ={\epsilon }_L+{\epsilon }_R+U$ and of the chemical potential $\mu$ of the normal leads for degenerate dots’ levels $\Delta \epsilon =0$. The large negative-differential-conductance peak is labeled by the symbol “$-$.”The other parameters are: ${\Gamma }_S=0.5U$ and $k_{B}T=0.01U$.

Figure 4

(Color online) Density plot of the differential conductance in units of $G_{\text{tunn}}=\left(e^2/h\right){\Gamma }_N/\left(2\pi k_{B}T\right)$ as a function of the detuning $\delta ={\epsilon }_L+{\epsilon }_R+U$ and of the chemical potential $\mu$ of the normal leads for nondegenerate dots’ levels $\Delta \epsilon =0.25U$. The large negative-differential-conductance peak is labeled by the symbol $-$. The other parameters are: ${\Gamma }_S=0.5U$ and $k_{B}T=0.01U$.