Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling

TL;DR

This paper develops a non-equilibrium Green's function method to analyze electron-vibron interactions in single-molecule junctions, emphasizing the importance of including higher-order diagrams for accurate spectral and transport properties.

Contribution

The authors introduce a method that incorporates vertex corrections and polarization effects beyond the self-consistent Born approximation for electron-vibron coupling in molecular junctions.

Findings

Higher-order diagrams significantly affect spectral functions.

Going beyond SCBA is necessary for accurate transport predictions.

The method applies to various transport regimes and bias conditions.

Abstract

We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on non-equilibrium Green's functions to calculate both equilibrium and non-equilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.