Fermi liquid theory of resonant spin pumping

We study resonant all-electric adiabatic spin pumping through a quantum dot with two nearby levels by using a Fermi liquid approach in the strongly interacting regime, combined with a projective numerical renormalization group (NRG) theory. Due to spin-orbit coupling, a strong spin pumping resonance emerges at every charging transition, which allows for the transfer of a spin $\sim \hslash /2$ through the device in a single pumping cycle. Depending on the precise geometry of the device, controlled pure spin pumping is also possible.

Figure 1

Sketch of the spin pumping cycle. In the initial configuration one electron is injected into the dot. Due to the spin orbit interaction the spin up and spin down parts of the wave function are rotated differently (for clarity, only the spin up component is shown), and the spin up and spin down parts move into different electrodes, thereby resulting in spin pumping.

Figure 2

Comparison of the projected NRG and full DM-NRG results for the total occupation of the dot for $\varepsilon ={\varepsilon }_1\equiv {\varepsilon }_2$ for couplings $v_1^L=0.33\sqrt{\Gamma }$, $v_1^R=0.37\sqrt{\Gamma }$, $v_2^L=0.42\sqrt{\Gamma }$, and $v_2^R=-0.46\sqrt{\Gamma }$. The Coulomb energy is $U=2\Gamma$, $\alpha =0.9\Gamma$, and $t=0.2\Gamma$.

Figure 3

(a) Density plot for the total occupation number in the $[\overline{\varepsilon },\Delta \varepsilon ]$ plane for the same parameters as in Fig. 2. (b) Dimensionless spin field ${\Gamma }^2{\Pi }_L^{\left(S\right)}(\overline{\varepsilon },\Delta \varepsilon )$ for the same parameters. The dashed black triangle indicates the pumping cycle used in Fig. 4. Figure 1 shows the cycle indicated by dotted black lines. Dash-dotted blue lines denote the mixed valence regimes, where the total occupation is $\langle n\rangle =0.5$ ($\langle n\rangle =1.5$).

Figure 4

Pumped charge and spin per cycle as function of the hybridization $t$ of the two levels, as computed for the triangle-shaped cycle in Fig. 3b. The couplings are fixed to $v_1^L=0.33\sqrt{\Gamma }$, $v_1^R=0.37\sqrt{\Gamma }$, $v_2^L=0.42\sqrt{\Gamma }$, and $v_2^R=-0.46\sqrt{\Gamma }$. $\langle S_z\rangle$ is measured in units of $\hslash /2$ and the pumped charge $\langle Q\rangle$ in units of e.

Figure 5

Sketch of the occupation of the dot and the position of the spin pumping resonances.