Perfect spin polarization in T-shaped double quantum dots due to the spin-dependent Fano effect

We study the spin-resolved transport properties of T-shaped double quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we calculate the linear conductance and the spin polarization of the current for various model parameters and at different temperatures. We show that an effective exchange field due to the presence of ferromagnets results in different conditions for Fano destructive interference in each spin channel. This spin dependence of the Fano effect leads to perfect spin polarization, the sign of which can be changed by tuning the dots' levels. Large spin polarization occurs due to Coulomb correlations in the dot, which is not directly coupled to the leads, while finite correlations in the directly coupled dot can further enhance this effect. Moreover, we complement accurate numerical results with a simple qualitative explanation based on analytical expressions for the zero-temperature conductance. The proposed device provides a prospective example of an electrically controlled, fully spin-polarized current source, which operates without an external magnetic field.

Figure 1

The spin-resolved linear conductance, $G_{\sigma }$, the total conductance, $G$, and the spin polarization, $\mathcal{P}$, obtained by the numerical renormalization group method, as a function of the first dot level ${\varepsilon }_1$ for typical DQD parameters indicated in the figure. The spin-dependent Fano effect leads to perfect spin polarization, the sign of which can be controlled by tuning the dot level position. See Sec. 2 for details of the model and method.

Figure 2

The spin-resolved linear conductance (first row) and the spin polarization (second row) as a function of ${\varepsilon }_2$ for two values of ${\varepsilon }_1$, as indicated, and for $t=2\Gamma$ in the case of noninteracting DQDs. The left column corresponds to $p=0.4$ and $B=0$, while the right column to $p=0$ and $B=\Gamma$.

Figure 3

The normalized spectral function of the second dot ${\mathcal{A}}_2\left(\omega \right)$ plotted as a function of energy $\omega$ and position of the second dot level ${\varepsilon }_2$ for (a) ${\varepsilon }_1=0$, (b) ${\varepsilon }_1=-0.05\Gamma$, (c) ${\varepsilon }_1=-0.1\Gamma$, (d) ${\varepsilon }_1=-0.15\Gamma$, (e) ${\varepsilon }_1=-0.2\Gamma$, and (f) ${\varepsilon }_1=-0.25\Gamma$. The dashed lines present the results obtained from analytical formula (20). The parameters are $U_1=0$, $U_2=U=0.5$, $\Gamma =U/5$, $t=\Gamma /2$, and $p=0.4$.

Figure 4

The linear conductance (first row) and the spin polarization (second row) as a function of ${\varepsilon }_1$ for $\Gamma /U=0.1$ (left column) and $\Gamma /U=0.2$ (right column) calculated for different values of the hopping $t$ between the dots, as indicated. The parameters are $U_1=0$, $U_2=U=0.5$, ${\varepsilon }_2=-U/3$, $p=0.4$, and $T=0$.

Figure 5

(a) and (b) The spin-resolved and total conductances, and (c) and (d) the spin-dependent occupations together with the self-energies for $\omega =0$ of the side-coupled quantum dot as a function of ${\varepsilon }_1$ calculated by NRG for $\Gamma /U=0.2$, $t=0.7\Gamma$ (left column), and $t=\Gamma$ (right column). The vertical dotted lines mark the positions where the minima in spin-dependent conductance occur. The horizontal lines correspond to $-{\varepsilon }_2/U_2=1/3$ and $1/2$. The minimum of $G_{\sigma }$ occurs at the crossing of ${\Sigma }_{2\sigma }\left(0\right)/U_2$ with $1/3$; cf. Eq. (15). The Friedel sum rule predicts the minimum to occur when $\langle n_{2\sigma }\rangle =1/2$. The other parameters are the same as in Fig. 4.

Figure 6

The spin polarization $\mathcal{P}$ (a) and the logarithm of the linear conductance $G$ (b), $G_{\uparrow }$ (c), and $G_{\downarrow }$ (d) as a function of ${\varepsilon }_1$ and $t$ calculated for parameters the same as in Fig. 4 with $\Gamma /U=0.2$.

Figure 7

The linear conductance (a) and the spin polarization (b) as a function of the first dot detuning ${\delta }_1$ calculated for different Coulomb correlations in the first dot, as indicated. The other parameters are $U_2=0.5$, $\Gamma =t=U_2/5$, ${\varepsilon }_2=-U_2/3$, $p=0.4$, and $T=0$.

Figure 8

The spin polarization as a function of the DQD levels ${\varepsilon }_1$ and ${\varepsilon }_2$ calculated for $U_1=U_2=U=0.5$. The other parameters are the same as in Fig. 7.

Figure 9

The linear conductance (a) and the spin polarization (b) as a function of ${\delta }_1$ calculated for different temperatures $T$ and for $U_1=U_2=U=0.5$. The inset in (b) presents the temperature dependence of $\mathcal{P}$ for ${\delta }_1=0$ and ${\delta }_1/\Gamma =-0.48$. The other parameters are the same as in Fig. 7.