Nonequilibrium Kondo Effect in a Quantum Dot Coupled to Ferromagnetic   Leads
  We study the Kondo effect in the electron transport through a quantum dot coupled to ferromagnetic leads, using a real-time diagrammatic technique which provides a systematic description of the nonequilibrium dynamics of a system with strong local electron correlations. We evaluate the theory in an extension of the `resonant tunneling approximation', introduced earlier, by introducing the self-energy of the off-diagonal component of the reduced propagator in spin space. In this way we develop a charge and spin conserving approximation that accounts not only for Kondo correlations but also for the spin splitting and spin accumulation out of equilibrium. We show that the Kondo resonances, split by the applied bias voltage, may be spin polarized. A left-right asymmetry in the coupling strength and/or spin polarization of the electrodes significantly affects both the spin accumulation and the weight of the split Kondo resonances out of equilibrium. The effects are observable in the nonlinear differential conductance. We also discuss the influence of decoherence on the Kondo resonance in the frame of the real-time formulation. 
Yasuhiro Utsumi, Jan Martinek, Gerd Sch\"on, Hiroshi Imamura,   Sadamichi Maekawa