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The interplay of dynamical nuclear polarization (DNP) and leakage current through a double quantum dot in the spin-blockade regime is analyzed. A finite DNP is built up due to a competition between hyperfine (HF) spin-flip transitions and another inelastic escape mechanism from the triplets, which block transport. We focus on the temperature dependence of the DNP for zero energy detuning (i.e., equal electrostatic energy of one electron in each dot and a singlet in the right dot). Our main result is the existence of a transition temperature, below which the DNP is bistable, so a hysteretic leakage current versus external magnetic field B appears. This is studied in two cases: (i) close to the crossing of the three triplet energy levels near B = 0, where spin-blockade is lifted due to the inhomogeneity of the effective magnetic field from the nuclei. (ii) At higher B-fields, where the two spin-polarized triplets simultaneously cross two different singlet energy levels. We develop simplified models leading to different transition temperatures T-c,T-TT and T-c,T-ST for the crossing of the triplet levels and the singlet-triplet level crossings, respectively. We find T-c,T-TT analytically to be given solely by the HF couplings, whereas T-c,T-ST depends on various parameters and T-c,T-ST > T-c,T-TT. The key idea behind the existence of the transition temperatures at zero energy detuning is the suppression of energy absorption compared to emission in the inelastic HF transitions. Finally, by comparing the rate equation results with Monte Carlo simulations, we discuss the importance of having both HF interaction and another escape mechanism from the triplets to induce a finite DNP.
carbon nanotubes; spontaneous emission; electron relaxation; transport; nanostructures; spectroscopy; resonance; spectrum; field