Hysteretic behavior in weakly coupled double-dot transport in the spin blockade regime

Double quantum dot systems in the spin blockade regime exhibit leakage currents that have been attributed to the Hyperfine interaction. We model weakly coupled double-dot transport using a rate equation approach which accounts for Hyperfine flip-flop transitions. The rate equations allow us to obtain self-consistently the time evolution for electronic charge occupations and for the nuclei polarizations in each dot. We analyze the current in the spin blockade region as a function of magnetic field and observe hysteretic behavior for fields corresponding to the crossing between triplet and singlet states.