Large-voltage behavior of charge transport characteristics in nanosystems with weak electron-vibration coupling.

Tomáš Novotný,Wolfgang Belzig

doi:10.3762/bjnano.6.188

Abstract

We study analytically the Full Counting Statistics of the charge transport through a nanosystem consisting of a few electronic levels weakly coupled to a discrete vibrational mode. In the limit of large transport voltage bias the cumulant generating function can be evaluated explicitly based solely on the intuitive physical arguments and classical master equation description of the vibration mode. We find that for the undamped vibrational modes mutual dynamical interplay between electronic and vibronic degrees of freedom leads to strongly nonlinear (in voltage) transport characteristics of the nanosystem. In particular, we find that for large voltages the k-th cumulant of the current grows as V2k to be contrasted with the linear dependence in case of more strongly externally damped and thus thermalized vibrational modes.

Highlights

The study of inelastic effects in transport through nanostructures, in particular in molecules [1,2,3] or atomic wires [4,5] has been an active field of research in past decade
Theoretical modeling of inelastic electron tunneling spectroscopy (IETS) signals usually proceeds via combination of ab initio structural density functional theory (DFT) calculations determining the parameters of an effective electron–vibrational Hamiltonian with the non-equilibrium Green’s functions (NEGF) evaluation of the IETS features [10]
Apart from a full NEGF description in terms of coupled electronic and vibrational Green’s functions [15,16] necessary for intermediate coupling, a simple rate equation for the occupation of the vibrational mode(s) was developed and successfully employed to IETS current in the weak coupling regime [11]. This method of mean-field-like accounting for nonequilibrium vibrational occupation cannot be used directly in the calculation of higher-order current cumulants starting with the electronic current noise since it neglects important correlation effects between the electronic and vibronic degrees of freedom, which are relevant even in the weak coupling regime [17]. After realizing this issue there have been several attempts to address this problem within a lowest order expansion (LOE)-like type of formalism, which would be valid in the weak coupling regime only but which would use simplifiedanalytical formulas for the IETS features with non-equilibrated phonons

Summary

Introduction

The study of inelastic effects in transport through nanostructures, in particular in molecules [1,2,3] or atomic wires [4,5] has been an active field of research in past decade. This method of mean-field-like accounting for nonequilibrium vibrational occupation cannot be used directly in the calculation of higher-order current cumulants starting with the electronic current noise since it neglects important correlation effects between the electronic and vibronic degrees of freedom, which are relevant even in the weak coupling regime [17].

Results

Conclusion