Splitting and Restoration of Kondo Peak in a Deformed Molecule Quantum Dot Coupled to Ferromagnetic Electrodes

We adopt the nonequilibrium Green’s function method to theoretically study the Kondo effect in a deformedmolecule, which is treated as an electron-phonon interaction (EPI) system. The self-energy for phonon part is calculatedin the standard many-body diagrammatic expansion up to the second order in EPI strength. We find that the multiplephonon-azsisted Kondo satellites arise besides the usual Kondo resonance. In the antiparallel magnetic configuration thesplitting of main Kondo peak and phonon-assisted satellites only happen for asymmetrical dot-lead couplings, but it isfree from the symmetry for the parallel magnetic configuration. The EPI strength and vibrational frequency can enhancethe spin splitting of both main Kondo and satellites. It is shown that the suppressed zero-bias Kondo resonance canbe restored by applying an external magnetic field, whose magnitude is dependent on the phononic effect remarkably.Although the asymmetry in tunnel coupling has no contribution to the restoration of spin splitting of Kondo peak, itcan shrink the external field needed to switch tunneling magnetoresistance ratio between large negative dip and largepositive peak.