Modeling inelastic phonon scattering in atomic- and molecular-wire junctions

Abstract

Computationally inexpensive approximations describing electron-phonon scattering in molecularscale conductors are derived from the non-equilibrium Green's function method. The accuracy is demonstrated with a first principles calculation on an atomic gold wire. Quantitative agreement between the full non-equilibrium Green's function calculation and the newly derived expressions is obtained while simplifying the computational burden by several orders of magnitude. In addition, analytical models provide intuitive understanding of the conductance including non-equilibrium heating and provide a convenient way of parameterizing the physics. This is exemplified by fitting the expressions to the experimentally observed conductances through both an atomic gold wire and a hydrogen molecule.

Transmission eigenchannels from nonequilibrium Green’s functions

“…In addition, the method gives a useful basis to understand the effects of phonon scattering on the conductance and their propensity rules. 25,26 …”

“…21 Related to our approach is the so-called ͑left and/or right͒ open "channel functions" of Inglesfield et al based on the "embedding potential" in the real-space formulation 22 and the Korringa-Kohn-Rostokerbased formulation by Bagrets et al 23,24 In addition to providing a simple way to calculate the eigenchannels, the method presented here offers an intuitive understanding of the oneparticle NEGF equations; e.g., it may be used to understand propensity rules for the effect of phonon scattering on the electronic transport. 25,26 The paper is organized as follows. Section II starts with the definition of eigenchannels and a summary of the standard one-particle NEGF equations.…”

Molecular signature of highly conductive metal-molecule-metal junctions

“…Moreover simple molecular junctions can be described to higher accuracy by theoretical calculations due to the limited size of these physical systems. The simplicity of the electronic structure may help to validate different approximations [18][19][20][21] that simplify the calculations and provide intuitive models. 19,22,23 Consequently the comparison between theory and experiment is more straightforward.…”

Inelastic transport theory from first principles: Methodology and application to nanoscale devices

“…We also describe approximations leading to a lowest order expansion ͑LOE͒ of the SCBA expressions, which vastly simplifies the computational burden. 47,48 While there have already been many studies devoted to transport with e-ph interaction based on model Hamiltonians emphasizing various aspects of the transport, [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] there has only been a handful based on a complete first-principles description of all aspects of the e-ph transport problem ͑de-scribed below͒. By this distinction we intend to emphasize approaches where structural, vibrational, and transport properties are derived from the knowledge of the elemental constituents only, i.e., without any system-dependent adjustable parameters.…”

“…Their results compare well with experiments by Kushmerick et al 21 During the development of the scheme presented here, we studied the same molecular systems with similar results. 47,78 We also used it to model inelastic effects that can be observed in atomic gold wires. 80 The paper is organized as follows.…”