Influence of vibrational modes on quantum transport through a nanodevice

Abstract

We employ the recently proposed scattering states numerical renormalization group (SNRG) approach to calculate $I(V)$ and the differential conductance through a single molecular level coupled to a local molecular phonon using the spinless Anderson-Holstein model. We also discuss the equilibrium physics of the model and demonstrate that the low-energy Hamiltonian is given by an effective interacting resonant level model. From the NRG level flow, we directly extract the effective charge transfer scale ${\ensuremath{\Gamma}}_{\mathrm{eff}}$ and the dynamically induced capacitive coupling ${U}_{\mathrm{eff}}$ between the molecular level and the lead electrons, which turns out to be proportional to the polaronic energy shift ${E}_{p}$ for the regimes investigated here. The equilibrium spectral functions for the different parameter regimes are discussed. The additional phonon peaks at multiples of the phonon frequency ${\ensuremath{\omega}}_{0}$ correspond to additional maxima in the differential conductance. Nonequilibrium effects, however, lead to significant deviations between a symmetric junction and a junction in the tunnel regime. The suppression of the current for particle-hole asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed.