Phonon anharmonic frequency shift induced by four-phonon scattering calculated from first principles

TL;DR

This study rigorously calculates phonon energy shifts in silicon due to anharmonic four-phonon scattering from first principles, revealing the importance of higher-order anharmonicity for optical phonons and the sensitivity of frequency shifts to force constant cutoff radii.

Contribution

It introduces a first-principles method to compute four-phonon scattering effects on phonon frequencies, emphasizing the significance of cutoff radius and higher-order anharmonicity.

Findings

Frequency shifts agree with neutron scattering data.

Optical phonon shifts are sensitive to cutoff radius.

Higher-order anharmonicity is crucial for optical phonons.

Abstract

Phonon energies at finite temperatures shift away from their harmonic values due to anharmonicity. In this paper, we have realized the rigorous calculation of phonon energy shifts of silicon by three and four-phonon scattering from first principles. The anharmonic fourth-order force constants are calculated by considering up to the fifth nearest neighbors. The results agree reasonably well with available data from inelastic neutron scattering throughout the Brillouin zone. Surprisingly, the frequency shifts of optical phonon modes near the $\Gamma$ point are sensitive to the cutoff radius of the fourth-order force constants, in contrast to the four-phonon scattering rates, which nearly saturate when considering the second nearest neighbors. We have also compared the results with ab initio molecular dynamics simulations and found that the higher order of anharmonicity is important for optical phonons. Our work provides critical insight into the anharmonic phonon frequency shift and will have significant impact on the thermal and optical applications.