Influence of vibrational modes on the quantum transport through a nano-device

TL;DR

This paper investigates how vibrational modes influence quantum transport in nano-devices using the SNRG method, revealing effects like phonon peaks, Franck-Condon blockade, and effective Hamiltonian parameters.

Contribution

It introduces the application of the SNRG approach to analyze vibrational effects on quantum transport and derives effective models and parameters from the NRG level flow.

Findings

Effective charge transfer scale $ ext{Gamma}_{ m eff}$ proportional to polaronic energy shift $E_p$

Phonon peaks at multiples of phonon frequency $ ext{w}_0$ in spectral functions

Suppression of current in asymmetric junctions with increasing electron-phonon coupling

Abstract

We use 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. 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 $\Gamma_{\rm eff}$ and the dynamically induced capacitive coupling $U_{\rm eff}$ 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 $\w_0$ correspond to additional maxima in the differential conductance. Non-equilibrium effects, however, lead to significant deviations between a symmetric junction and a junction in the tunnel regime. The suppression of the current for asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed with a simple framework of a combination of (i) polaronic level shifts and (ii) the effective charge transfer scale $\Gamma_{\rm eff}$.