Phonon-assisted Kondo effect in a single-molecule transistor out of equilibrium

The joint effect of the electron–phonon interaction and Kondo effect on nonequilibrium transport through a single molecule transistor is investigated by using the improved canonical transformation scheme and extended equation of motion approach. Two types of Kondo phonon-satellite with different asymmetric shapes are fully confirmed in the spectral function, and are related to the electron spin singlet or hole spin singlet, respectively. Moreover, when a moderate Zeeman splitting is caused by a local magnetic field, the Kondo satellites in the spin-resolved spectral function are found to disappear on one side of the main peak, and they disappear on the opposite side for the opposite spin component. All these peculiar signatures that manifest themselves in the nonlinear differential conductance are explained with a clear physics picture.