A Computational Method for Studying Vibrational Mode Dynamics

TL;DR

This paper introduces a novel formalism for analyzing phonon transport in solids, enabling real-time observation of energy exchange between vibrational modes during molecular dynamics simulations, which enhances understanding of heat transfer mechanisms.

Contribution

It presents a new method that projects interatomic interactions onto normal modes, revealing real-time phonon interactions beyond traditional correlation-based approaches.

Findings

Energy exchange occurs through specific mode interaction channels.

Only a small fraction of interaction pathways transfer significant energy.

The method provides new insights into phonon transport in superlattices.

Abstract

The traditional picture of heat transfer in solids by atomic vibrations, also known as phonons, involves phonons scattering with each other like gas particles and is commonly referred to as the phonon gas model (PGM). This physical picture accounts for interactions among propagating (i.e., plane wave modulated) vibrational modes in an ideal crystal, but it becomes problematic when describing non-propagating modes arising in realistic non-idealized systems. Here, we introduce a more general formalism for studying phonon transport, which involves projection of the interatomic interactions themselves (i.e., not just the atom motion), onto the normal modes of the system. This shows, for the first time, how energy is exchanged between modes in real-time during molecular dynamics (MD) simulations, as opposed to other MD methods which use inferences based on correlations, or other time averaged schemes that do not preserve specific features in the real-time dynamics. Applying this formalism to the example case of modes interacting in a superlattice, we illustrate a new perspective on how phonon transport occurs, whereby individual normal modes share energy through specific channels of interaction with other modes. We also highlight that while a myriad of interaction pathways exist, only a tiny fraction of these pathways actually transfer significant amounts of energy, which is surprising. The approach allows for the prediction and simulation of these mode/phonon interactions, thus unveiling the real-time dynamics of phonon behavior and advancing our ability to understanding and engineer phonon transport.