Dynamical nuclear spin polarization in a quantum dot with an electron spin driven by electric dipole spin resonance

We analyze the polarization of nuclear spins in a quantum dot induced by a single-electron spin that is electrically driven to perform coherent Rabi oscillations. We derive the associated nuclear-spin polarization rate and analyze its dependence on the accessible control parameters, especially the detuning of the driving frequency from the electron Larmor frequency. The arising nuclear-spin polarization is related to the Hartmann-Hahn effect known from the NMR literature with two important differences. First, in quantum dots, one typically uses a micromagnet, leading to a small deflection of the quantization axes of the electron and nuclear spins. Second, the electric driving wiggles the electron with respect to the atomic lattice. The two effects, absent in the traditional Hartmann-Hahn scenario, give rise to two mechanisms of nuclear-spin polarization in gated quantum dots. The arising nuclear-spin polarization is a resonance phenomenon, achieving maximal efficiency at the resonance of the electron Rabi and nuclear Larmor frequency (typically a few or a few tens of MHz). As a function of the driving frequency, the polarization rate can develop sharp peaks and reach large values at them. Since the nuclear polarization is experimentally detected as changes of the electron Larmor frequency, we often convert the former to the latter in our formulas and figures. In these units, the polarization can reach hundreds of MHz/s in GaAs quantum dots and at least tens of kHz/s in Si quantum dots. We analyze possibilities to exploit the resonant polarization effects for achieving large nuclear polarization and for stabilizing the Overhauser field through feedback.