Local modes, phonons, and mass transport in solid $^4$He

TL;DR

This paper models local atomic motions in solid $^4$He as local modes within a self-consistent harmonic framework, revealing phase-dependent correlations, phonon hybridization, and implications for mass transport and specific heat.

Contribution

It introduces a model treating local atomic motions as local modes, providing a unified explanation for phonon behavior and mass transport in solid $^4$He without relying on vacancies.

Findings

In bcc phase, local motions are highly directional and correlated.

Hybridization of local modes with phonons explains phonon softening.

Predicts a high energy excitation branch relevant for self-diffusion.

Abstract

We propose a model to treat the local motion of atoms in solid $^{4}$He as a local mode. In this model, the solid is assumed to be described by the Self Consistent Harmonic approximation, combined with an array of local modes. We show that in the bcc phase the atomic local motion is highly directional and correlated, while in the hcp phase there is no such correlation. The correlated motion in the bcc phase leads to a strong hybridization of the local modes with the T$_{1}(110)$ phonon branch, which becomes much softer than that obtained through a Self Consistent Harmonic calculation, in agreement with experiment. In addition we predict a high energy excitation branch which is important for self-diffusion. Both the hybridization and the presence of a high energy branch are a consequence of the correlation, and appear only in the bcc phase. We suggest that the local modes can play the role in mass transport usually attributed to point defects (vacancies). Our approach offers a more overall consistent picture than obtained using vacancies as the predominant point defect. In particular, we show that our approach resolves the long standing controversy regarding the contribution of point defects to the specific heat of solid $^{4}$He.