Exploring the limits of the self consistent Born approximation for inelastic electronic transport

摘要

The non equilibrium Green function formalism is today the standardcomputational method for describing elastic transport in molecular devices.This can be extended to include inelastic scattering by the so calledself-consistent Born approximation (SCBA), where the interaction of theelectrons with the vibrations of the molecule is assumed to be weak and it istreated perturbatively. The validity of such an assumption and therefore of theSCBA is difficult to establish with certainty. In this work we explore thelimitations of the SCBA by using a simple tight-binding model with theelectron-phonon coupling strength $\rm{\alpha}$ chosen as a free parameter. Asmodel devices we consider Au mono-atomic chains and a $\rm{H_2}$ moleculesandwiched between Pt electrodes. In both cases our self-consistentcalculations demonstrate a breakdown of the SCBA for large $\rm{\alpha}$ and weidentify a weak and strong coupling regime. For weak coupling our SCBA resultscompare closely with those obtained with exact scattering theory. However inthe strong coupling regime large deviations are found. In particular wedemonstrate that there is a critical coupling strength, characteristic of thematerials system, beyond which multiple self-consistent solutions can be founddepending on the initial conditions in the simulation. We attribute thesefeatures to the breakdown of the perturbative expansion leading to the SCBA.