We analyzed the electronic transport through a double quantum dot in the spin blockade regime. Experiments of current rectification by Pauli exclusion principle in double quantum dots were discussed. The electron and nuclei spin dynamics and their interplay due to the hyperfine interaction were self-consistently analyzed within the framework of rate equations. Our results show that the current leakage experimentally observed in the spin-blockade region is due to spin-flip processes induced by hyperfine interaction through Overhauser effect. We show as well how a magnetic field applied parallel to the current allows excited states to participate in the electronic current and removes spin blockade. Our model includes also a self-consistent description of inelastic transitions where the energy is exchanged through interactions with acoustic phonons in the environment. It accounts for spontaneous emission of phonons which results in additional features in the current characteristics. We develop a microscopical model to treat the hyperfine interaction in each dot. Using this model, we study the dynamical nuclear polarization as a function of the applied voltage.

• Received 22 May 2007

DOI:https://doi.org/10.1103/PhysRevB.76.085329