Quantum dot as a spin-current diode: A master-equation approach

We report a study of spin-dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead (NM-QD-FM). We use the master equation approach to calculate the spin-resolved currents in the presence of an external bias and an intradot Coulomb interaction. We find that for a range of positive external biases (current flow from the normal metal to the ferromagnet) the current polarization $\wp =(I_{\uparrow }-I_{\downarrow })∕(I_{\uparrow }+I_{\downarrow })$ is suppressed to zero, while for the corresponding negative biases (current flow from the ferromagnet to the normal metal) $\wp$ attains a relative maximum value. The system thus operates as a rectifier for spin-current polarization. This effect follows from an interplay between Coulomb interaction and nonequilibrium spin accumulation in the dot. In the parameter range considered, we also show that the above results can be obtained via nonequilibrium Green functions within a Hartree-Fock type approximation.

Figure 1

System studied: a nonmagnetic quantum dot coupled via tunneling barriers to a nonmagnetic left lead and a ferromagnetic right lead. A bias voltage $V$ is applied across the system so that the left $\left({\mu }_L\right)$ and right $\left({\mu }_R\right)$ chemical potentials differ by ${\mu }_L-{\mu }_R=eV$.

Figure 2

Current polarization $\wp$ as a function of the external bias. For $p$ values between 0.2 and 0.9, $\wp$ reaches zero for some particular positive bias range, while for the negative counterpart it reaches maximum plateaus.

Figure 3

Spin accumulation $m=n_{\uparrow }-n_{\downarrow }$ as a function of the external bias. For $p=0$ (unpolarized lead) there is no spin accumulation in the dot. When $p$ increases the spin accumulation increases as well becoming negative for $eV>0$ and positive for $eV<0$.

Figure 4

Spin-resolved currents against bias voltage. For the plateaus indicated by arrows, $I_{\uparrow }$ lies on top of $I_{\downarrow }$. This gives rise to the $\wp =0$ plateau seen in Fig. 2. For big enough polarizations (e.g., $p>0.8$) a negative-differential resistance range arises in the spin-up current.

Figure 5

Current polarization $\wp$ as a function of the bias voltage for the asymmetry parameters $x=0.2$ (upper panel) and $x=0.8$ (bottom panel). We observe that the $\wp =0$ plateau enlarges for $x=0.2$ and shrinks for $x=0.8$ when compared to the $x=0.5$ case. In contrast, the maximum plateau $\wp =p$ reduces for $x=0.2$ and enlarges for $x=0.8$ when compared to the $x=0.5$ case.