Non-equilibrium Kondo effect in a quantum dot coupled to two metallic leads is studied theoretically. The leads can be either ferromagnetic or nonmagnetic. However, of particular interest is the case when the leads are made of a system with large spin asymmetry of transport properties, like giant and/or colossal magnetoresistance materials. Owing to the spin asymmetry, the effective coupling between the dot and reservoirs can be strongly spin dependent, too. Electron interaction on the dot is taken into account via the Hubbard term for a single-channel model with an arbitrary value of the correlation parameter U.
The non-equilibrium Green function technique is used to calculate electric current and density of states. The key point of the approach is a consistency of the approximations used to calculate the lesser and retarded (advanced) Green functions within the equation of motion method. These functions are calculated on equal footing, ie, within the same approximation scheme. The description generalizes in several ways some of the earlier descriptions based on the equation of motion method. (i) It applies to nonmagnetic and magnetic systems. (ii) The description is gauge invariant (the electrostatic potential due to the charge on the dot is included). (iii) It applies to equilibrium as well non-equilibrium situations.
The key difference between our approach and some of the earlier descriptions based on the equation of motion technique originates from a difference in the predictions on the occupation numbers. This difference gives rise to a difference in the density of states at the Fermi level as well as in the corresponding Kondo anomaly in the differential conductance at small bias. The difference is particularly large in the case of asymmetric junctions, even in equilibrium situations. The model predicts spin splitting of the Kondo peak in the density of states in the magnetic case, as well as some anomalous behavior in external magnetic field.

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