Considering phonon particle-wave duality in materials design

Atomic vibrations are an integral part of material behavior, from storing/transporting thermal energy and contributing to the thermodynamic state of the material to enabling structural phase transformations and facilitating atomic diffusion, as well as being a key contributor to electronic transport processes and light-matter interactions. As ultrafast experimental techniques increasingly probe localized excited states on femtosecond timescales, it is important to review the theoretical framework that bridges mode-space theory and real-space, time-resolved atomic motion. Vibrational energy, quantized as phonons, forms the basis for theoretical predictions of dynamical properties. Conventional lattice dynamics describes vibrations as delocalized plane waves with amplitudes set by the average thermal phonon occupations, and thus does not capture the time evolution of local fluctuations. Herein, it is demonstrated how lattice dynamics extends to a wave packet formalism required to explain much of the particle-like behavior of phonons, where a wave packet is defined as a coherent superposition of phonons. Specifically, vibrational modes having neighboring wave vectors have in-phase phonon excitations until coherence is lost due to phonon scattering. Fluctuations arise from the continual exchange of energy (phonons) between vibrational modes, corresponding to the formation and decay of wave packets. This unified lattice dynamics consideration of vibrational wave packets can complement molecular dynamics studies to probe the local fluctuation dynamics relevant to uncovering design principles for solid-state diffusion, thermal conductivity, and electronic transport in advanced materials.