We compute the anharmonic shift of the phonon frequencies in MgB2, using density functional theory. We explicitly take into account the scattering between different phonon modes at different q-points in the Brillouin zone. The shift of the E2g mode at the Gamma point is +5 % of the harmonic frequency. This result comes from the cancellation between the contributions of the four- and three-phonon scattering, respectively +10 % and -5 %. A similar shift is predicted at the A point, in agreement with inelastic X-ray scattering phonon-dispersion measurements. A smaller shift is observed at the M point.
@article{arxiv.cond-mat/0306650,
title = {Anharmonic phonon frequency shift in MgB2},
author = {Michele Lazzeri and Matteo Calandra and Francesco Mauri},
journal= {arXiv preprint arXiv:cond-mat/0306650},
year = {2009}
}