Phonon Assisted Tunneling in Framework of Minimal Model for Molecular Device in Adiabatic and Nonadiabatic Regimes

Abstract

Molecular devices are centered on finite bias transport. We have presented the crossover from antiadiabatic to the adiabatic regime of phonon assisted tunneling in the framework of a minimal model for molecular devices. A resonant level coupled by displacement to a single localized vibrational mode was found. It was found that the crossover from the polaronic of the antiadiabatic limit to the perturbative of the adiabatic regime was followed by the polaronic shift rather than the phonon frequency. The perturbative adiabatic limit was made as the bare hopping rate exceeded the polaronic shift leaving an extended window of coupling exceeded the phonon frequency. In extended antiadiabatic regimes the effective low energy Hamiltonian at energies below phonon frequency was purely fermionic and depended at resonance on two parameters tunneling amplitude and effective coulomb repulsion. The effective tunneling amplitude obeyed the empirical scaling for the extended antiadiabatic regime. The resonant phonon assisted tunneling and the relevant measurement of electronic motion was obtained by tunneling rate. The two limits corresponded to the bare electronic tunneling rate either sufficiently small or large in comparison to phonon frequency. It was found that phonon efficiently responded to hopping events by forming a polaron, suppressed the electronic tunneling rate and suppression produced narrow tunneling resonance. The phonon was found slow to respond to the frequent tunneling events having little effect on their rate. In this study framework of the Lang-Firsov transformation was considered by using ordinary perturbation theory of electron-phonon coupling. The obtained results found in good agreement with previously obtained result