Early experiments on spin-blockaded double quantum dots revealed surprising robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias [see e.g. K. Ono, S. Tarucha, Phys. Rev. Lett. 92, 256803 (2004)]. Experimental evidence strongly indicates that dynamical nuclear polarization plays a central role, but the mechanism has remained a mystery. Here we introduce a minimal albeit realistic model of coupled electron and nuclear spin dynamics which supports robust self-sustained oscillations. Our mechanism relies on a nuclear-spin analog of the tunneling magnetoresistance phenomenon (spin-dependent tunneling rates in the presence of an inhomogeneous Overhauser field) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The extremely long oscillation periods (up to hundreds of seconds) observed in experiments as well as the differences in phenomenology between vertical and lateral quantum dot structures are naturally explained in the proposed framework.
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