Beyond the Generalized Kadanoff–Baym Ansatz

Abstract

The study of electron transport is easier if the Kadanoff–Baym equations (KBE) are simplified using the Generalized Kadanoff–Baym Ansatz (GKBA). For molecular bridges, GKBA is empirically known to safely work for weak and flat tunneling functions. It fails, if either of the conditions is not satisfied. The case in point is a molecular bridge formed by an Anderson type local center treated in the mean field and linked by tunneling junctions to two ferromagnetic electrodes whose tunneling functions simulate nickel with complex sd structure. Transient magnetic currents under a constant galvanic bias between electrodes are invoked by sudden switching on of both junctions. We consider three tasks: To establish quantitative criteria for the validity of the Ansatz; to develop a practically tractable correction to the Ansatz working beyond its validity range; to obtain Generalized Master Equations (GMEs) for the one‐electron distribution following from both GKBA and its corrected form avoiding thus KBE. All three points are resolved by treating first the stationary (non‐equilibrium) limit and transferring the results to finite times. The corrections to the Ansatz are obtained as a stationary approximation to the vertex part of the exact reconstruction equations whose free term is the standard GKBA.