A simple approximation to the electron-phonon interaction in population dynamics

Carlos M. Bustamante, Tchavdar N. Todorov, Cristián G. Sánchez, Andrew Horsfield, Damian A. Scherlis

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Abstract

The modelling of coupled electron-ion dynamics including a quantum description of the nuclear degrees of freedom has remained a costly and technically difficult practice. The Kinetic Model for electron-phonon interaction provides an efficient approach to this problem, for systems evolving with low amplitude fluctuations, in a quasi-stationary state. We propose in this work an extension of the Kinetic Model to include the effect of coherences, which are absent from the original approach. The new scheme, referred to as Liouville von Neumann - Kinetic Equation (or LvN+KE), is implemented here in the context of a tight-binding Hamiltonian and employed to model the broadening, caused by the nuclear vibrations, of the electronic absorption bands of an atomic wire. The results, which show close agreement with the predictions given by Fermi’s Golden Rule, serve as a validation of the methodology. Thereafter, the method is applied to the electron-phonon interaction in transport simulations, adopting to this end the driven Liouville von Neumann equation to model open quantum boundaries. In this case the LvN+KE model qualitatively captures the Joule heating effect and Ohm’s law. It however exhibits numerical discrepancies with respect to the results based on Fermi’s Golden Rule, attributable to the fact that the quasi-stationary state is defined taking into consideration the eigenstates of the closed system rather than those of the open boundaries system. The simplicity and numerical efficiency of this approach and its ability to capture the essential physics of the electron-phonon coupling make it an attractive route to first-principles electron-ion dynamics.
Original languageEnglish
Pages (from-to)234108-1 - 234108-10
Number of pages10
JournalJournal of Chemical Physics
Volume153
Early online date17 Dec 2020
DOIs
Publication statusEarly online date - 17 Dec 2020

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