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

Abstract

The non equilibrium Green function formalism is today the standard computational method for describing elastic transport in molecular devices. This can be extended to include inelastic scattering by the so called self-consistent Born approximation (SCBA), where the interaction of the electrons with the vibrations of the molecule is assumed to be weak and it is treated perturbatively. The validity of such an assumption and therefore of the SCBA is difficult to establish with certainty. In this work we explore the limitations of the SCBA by using a simple tight-binding model with the electron-phonon coupling strength α chosen as a free parameter. As model devices we consider Au mono-atomic chains and a H2 molecule sandwiched between Pt electrodes. In both cases our self-consistent calculations demonstrate a breakdown of the SCBA for large α and we identify a weak and strong coupling regime. For weak coupling our SCBA results compare closely with those obtained with exact scattering theory. However in the strong coupling regime large deviations are found. In particular we demonstrate that there is a critical coupling strength, characteristic of the materials system, beyond which multiple self-consistent solutions can be found depending on the initial conditions in the simulation. We attribute these features to the breakdown of the perturbative expansion leading to the SCBA.

Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

“…Also, very recent studies have shown that self-consistent Φ-derivable approximations can converge to unphysical solutions; [34][35][36][37][38][39][40][41][42][43][44]47,48 similar issues have been noted in the context of time-dependent simulations [40][41][42][43][44][47][48][49] using the Kadanoff-Baym equations, but can be remedied by introducing self-consistent contributions in controlled fashion. 43 Nevertheless, the use of self-consistent MBPT may be justified to some extent.…”

“…1 are retained while the Hartree diagrams are neglected. 34 In applications one also often neglects the real part of the electron-phonon Fock diagram. 74 These approximations work under the assumption of small polaron shifts.…”

Signatures of electron-magnon interaction in charge and spin currents through magnetic tunnel junctions: A nonequilibrium many-body perturbation theory approach

“…2(a) are equivalent to the so-called self-consistent Born approximation (SCBA) for the electronic self-energy considered in problems like e-ph interacting systems. [38][39][40][41][43][44][45][46][47] However, in the case of e-m interaction, one has to introduce additional bookkeeping in such diagrams to account for flipping of electron spin together with magnon emission or absorption, as illustrated in Fig. 2.…”

“…We note that in SCBA for e-ph interacting systems, Σ H is often neglected 41,46 due to being small and, therefore, having little effect on the final current (this becomes unwarranted for larger e-ph interaction strengths where SCBA breaks down 46 ). For the e-m interacting systems, the situation is much more complex because direct evaluation of Eq.…”

“…(13) can acquire arbitrary phase thereby requiring to consider full double time dependence ofΣ H . We relegate this to future studies, while here we retainΣ e−m (E) =Σ F (E) which is termed 46 Fock-only SCBA (F-SCBA). In the case of e-ph many-body systems driven far from equilibrium, phonon heating due to propagating electrons has been considered either phenomenologically using a rate equation for the phonon occupation, [40][41][42] or microscopically by using phonon GF with interacting self-energy truncated to the e-h polarization bubble diagram.…”