Collective nature of phonon energies in solids beyond harmonic oscillators

TL;DR

This paper challenges the traditional harmonic oscillator model of phonons in solids, showing that phonon energies are interdependent and collective even at room temperature, which impacts understanding of thermodynamics and transport.

Contribution

It provides evidence for the collective nature of phonon energies in silicon, questioning the assumption of independent harmonic oscillators in phonon models.

Findings

Phonon energies exhibit inter-mode dependence at 300 K.

Phonon energies are more collective than previously assumed.

Implications for thermodynamics and transport models.

Abstract

Phonon quasi-particles have been monumental in microscopically understanding thermodynamics and transport properties in condensed matter for decades. Phonons have one-to-one correspondence with harmonic eigenstates and their energies are often described by simple independent harmonic oscillator models. Higher order terms in the potential energy lead to interactions among them, resulting in finite lifetimes and frequency shifts, even in perfect crystals. However, increasing evidence including constant volume heat capacity different from the expected Dulong-Petit law suggests the need for re-evaluation of phonons having harmonic energies. In this work, we explicitly examine inter-mode dependence of phonon energies of a prototypical crystal, silicon, through energy covariance calculations and demonstrate the concerted nature of phonon energies even at 300 K, questioning independent harmonic oscillator assumptions commonly used for phonon energy descriptions of thermodynamics and transport.