Mesoscopic Effects in Adiabatic Spin Pumping

We show that temporal shape modulations (pumping) of a quantum dot in the presence of spin-orbital coupling lead to a finite dc spin current. Depending on the strength of the spin-orbit coupling, the spin current is polarized perpendicular to the plane of the two-dimensional electron gas, or has an arbitrary direction subject to mesoscopic fluctuations. We analyze the statistics of the spin and charge currents in the adiabatic limit for the full crossover from weak to strong spin-orbit coupling.

Figure 1

Current variance (in units of $I_0^2/2$) as a function of Zeeman coupling strength ($b={\tau }_{\mathrm{e}\mathrm{s}\mathrm{c}}/{\tau }_Z$) for a fixed value of SO coupling strengths $c_{\perp }=0.47$, and $c_{\parallel }=0.12$ taken from Ref. 14. The difference between $⟨I_{\mathrm{s},x}^2⟩$ and $⟨I_{\mathrm{s},z}^2⟩$ for large $b$ vanishes for $c_{\perp }\gg 1$. The inset shows a quantum dot with out of phase shape modulation, and a typical electron trajectory which gathers a Aharonov-Bohm flux depending on its perpendicular spin projection.