Prediction of resonant all-electric spin pumping with spin-orbit coupling

All-electric devices for the generation and filtering of spin currents are of crucial importance for spintronics experiments and applications. Here we consider a quantum dot with spin-orbit interaction coupled to two metallic leads. After analyzing, the conditions for having nonvanishing spin currents in an adiabatically driven two-terminal device, we focus on a dot with two resonant orbitals and we show by specific examples that both spin filtering and pure spin current generation can be achieved. Finally, we discuss the effect of the Coulomb interaction.

Figure 1

Level structure of the quantum dot. Due to the spin orbit field, ${\vec{\alpha }}_{so}$, pumping leads to charge and spin current.

Figure 2

(Color online) Upper Panels: Brouwer’s charge and spin field, $B_c^{{\epsilon }_1,{\epsilon }_2}$ and $B_s^{{\epsilon }_1,{\epsilon }_2}$, in the $\left[\left({\epsilon }_1-{\epsilon }_2\right),\left({\epsilon }_1+{\epsilon }_2\right)\right]$ plane for $v_{2L}=-v_{1R}=2v_{2R}=1.25v_{1L}=\sqrt{\Gamma /\left(2\pi \rho \right)}$, $\alpha /\Gamma =0.25$. Lower Panels: pumped spin through a symmetric dot (left) and pumped spin and charge through a nonsymmetric dot (right) as a function of the SO coupling $\alpha$ for a triangular cycle: $\left({\epsilon }_1+{\epsilon }_2\right)∊\left[0,10\alpha \right]$ and $\left({\epsilon }_1-{\epsilon }_2\right)∊\left[-\left({\epsilon }_1+{\epsilon }_2\right),{\epsilon }_1+{\epsilon }_2\right]$. In the symmetric dot case the tunnel couplings are $v_{2L}=-v_{1R}=v_{2R}=v_{1L}=\sqrt{\Gamma /\left(2\pi \rho \right)}$ while in the nonsymmetric dot case they are the same as those of the upper panel.

Figure 3

(Color online) Left Panel: Brouwer’s spin field $B_s^{{\Gamma }_L,\left({\epsilon }_1+{\epsilon }_2\right)}$ in the $\left[{\Gamma }_L,\left({\epsilon }_1+{\epsilon }_2\right)\right]$-plane for ${\Gamma }_{kM}=c_{kM}^2{\Gamma }_M$ with $k=1,2$ and $M=L,R$, $c_{1L}=c_{2L}=0.8$, $c_{1R}=0.7$, and $c_{2R}=0.6$. The two levels are assumed degenerate, ${\epsilon }_1-{\epsilon }_2=0$, and the coupling to the right lead is ${\Gamma }_R/\alpha =3$. Right Panel: pumped spin and charge for a rectangular cycle ${\Gamma }_L/\alpha ∊\left[0,5\right]$ and $\left({\epsilon }_1+{\epsilon }_2\right)/\alpha ∊\left[0,x\right]$ as a function of $x$.

Figure 4

(Color online) Sketch of the effect of interactions. In the regime ${ϵ}_1,{ϵ}_2>0$, where the dot occupancy is small the noninteracting theory applies.