Nonadiabatic Pumping through Interacting Quantum Dots

We study nonadiabatic two-parameter charge and spin pumping through a single-level quantum dot with Coulomb interaction. For the limit of weak tunnel coupling and in the regime of pumping frequencies up to the tunneling rates, $\Omega \lesssim \Gamma /\hslash$, we perform an exact resummation of contributions of all orders in the pumping frequency. As striking nonadiabatic signatures, we find frequency-dependent phase shifts in the charge and spin currents, which opens the possibility to control charge and spin currents by tuning the pumping frequency. This includes the realization of an effective single-parameter pumping as well as pure spin without charge currents.

Figure 1

(a) Charge-current amplitude ${\mathcal{I}}_Q^{\max }$ (thin solid line), its adiabatic approximation ${\mathcal{I}}_Q^{\max ,\mathrm{ad}}$ (dashed line), and phase shift $\Delta {\varphi }_Q$ (thick solid line) as a function of $\hslash \Omega /\overline{\Gamma }$. (b) Pumped current ${\mathcal{I}}_Q$ as a function of $\hslash \Omega /\overline{\Gamma }$ for $\varphi =0.2\pi$ (solid line), $\varphi =0.4\pi$ (dashed line), and $\varphi =0.6\pi$ (dash-dotted line). (c) Pumped charge current ${\mathcal{I}}_Q$ as a function of $\varphi$ for $\hslash \Omega /\Gamma =0.1$ (solid line), 0.5 (dashed line), and 0.8 (dash-dotted line). All currents in units of $e\beta \Delta {\Gamma }_L\Delta \epsilon /\hslash$. Other parameters: $\overline{\epsilon }=k_{B}T\ln 2$, $U=9\overline{\Gamma }$, $k_{B}T=3\overline{\Gamma }$, $p_R=0$, and ${\overline{\gamma }}_R=1/2$.

Figure 2

(a) Spin-current amplitude ${\mathcal{I}}_S^{\max }$ (thick line) and its adiabatic approximation ${\mathcal{I}}_S^{\max ,\mathrm{ad}}$ (thin line) as a function of $\hslash \Omega /\overline{\Gamma }$ for different values of $p_R$. (b) Phase shift $\Delta {\varphi }_S$ as a function of $\hslash \Omega /\overline{\Gamma }$ for different values of $p_R$. (c) Charge and spin currents ${\mathcal{I}}_{Q,S}$ as a function of $\hslash \Omega /\overline{\Gamma }$ with $p_R=0.4$ and $\varphi =\pi /9$ for weak pumping (thick line) and strong pumping (thin line, with $\Delta {\Gamma }_L=\Delta \epsilon =0.4\overline{\Gamma }$). Spin currents in units of $\beta \Delta {\Gamma }_L\Delta \epsilon /2$. Other parameters: $\overline{\epsilon }=k_{B}T\log 2$, $U=9\overline{\Gamma }$, $k_{B}T=3\overline{\Gamma }$, and ${\overline{\gamma }}_R=1/2$.