Nonmonotonic Fano factor and backscattering effects in single-molecule junctions

Rate equations are a common tool to describe the transport properties of weakly coupled single-molecule junctions. Here, we study the physics of the Anderson-Holstein model at a single vibronic resonance. We derive conditions on the Franck-Condon factors that the resonance increases or decreases the stationary current thus causing negative differential conductance. The role of backscattering of charge at vibronic resonances is also investigated. In strongly asymmetrically coupled devices backscattering causes the resonance to split into two. In symmetrically coupled devices, the Fano factor shows nonmonotonicities, which are related to correlations of forward and backward scattering of charge.