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

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.

The Driven Liouville von Neumann Approach to Electron Dynamics in Open Quantum Systems

“…In recent years, important advances have been made both in terms of understanding the formal foundation of the theory and its implementation, especially in conjunction with first-principles treatments and within multi-scale approaches. Further research opportunities await, not only in terms of novel applications, but also in terms of methodological development including, e. g., spinuncompensated and non-collinear spin treatments, timedependent bias and gate voltages, coupled electron-nuclear dynamics, [133,134,156,[161][162][163][164][165][166] and much more. Opportunities also await in improvements of the numerical algorithms and their implementations in state-of-the-art computational platforms.…”

“…Within the framework of the Born‐Oppenheimer approximation in the adiabatic limit, it was demonstrated that when a molecule has a weak vibronic coupling in vacuum, steady‐state current may not be achievable even for a very short molecular length and that molecular vibrations are manifested in the current fluctuations [133] . Furthermore, the approach reproduces qualitatively the Joule heating effect and predicts trends that are consistent with the microscopic version of Ohm's law, with some numerical deviations from Fermi's golden rule that remain to be addressed [134] …”

“…[133] Furthermore, the approach reproduces qualitatively the Joule heating effect and predicts trends that are consistent with the microscopic version of Ohm's law, with some numerical deviations from Fermi's golden rule that remain to be addressed. [134] Having established the DLvN methodology for simulating electron dynamics in open quantum systems, we now turn to discussing some of its recent applications. Within the realm of molecular electronics, molecular interferometry emerges as a promising direction for designing active components with unique functionalities.…”

Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory

“…The continuous improvement of the underlying TDDFT and TD-current DFT approximations ensures the increased accuracy and reliability of predictions made using the developed methodology. Future generalizations toward spin-uncompensated and non-collinear descriptions, as well as coupled electron-nuclear dynamics, ,− will extend the applicability of the DLvN approach to describe magnetization dynamics and decoherence under external time-dependent stimuli. This will pave the way for studying key dynamical phenomena, such as high-speed current switching and routing in molecular interferometers, transient dynamics, transport under time dependent bias voltages, coherent control using shaped pulses to obtain programed response, and transport-driven chemical reactivity …”

Plasmon-Induced Hot Carriers: An Atomistic Perspective of the First Tens of Femtoseconds

“…These approaches become intractable very fast due to their high-order polynomial scaling on the number of both electrons and phonons and therefore not presently applicable to the problem at hand. Interesting new work by Bustamante et al has recently shown promise to describe electron−phonon within a simple scheme, 39 and this is an avenue that we will likely take in the near future. The method combines a firstorder perturbation treatment of the electron−phonon energy exchange with the heuristic addition of appropriate and consistent damping terms on the electron density matrix.…”