Dynamical Self-Quenching of Spin Pumping into Double Quantum Dots

Nuclear spin polarization can be pumped into spin-blocked quantum dots by multiple Landau- Zener passages through singlet-triplet anticrossings. By numerical simulations of realistic systems including approximately $10^7$ nuclear spins during $10^5$ sweeps, we uncover a mechanism of dynamical self-quenching which results in a fast saturation of the nuclear polarization under stationary pumping. This is caused by screening of the field of the nuclear spins. In systems with moderate spin-orbit coupling, self-quenching also screens the spin-orbit interaction. The mechanism is generic and remains robust under a moderate noise. Our finding explains low polarization levels achieved experimentally and calls for developing new protocols that break the self-quenching limitations.