Electron-phonon coupling and phonon self-energy in ${\mathrm{MgB}}_{2}$: Interpretation of ${\mathrm{MgB}}_{2}$ Raman spectra

Electron-phonon coupling and phonon self-energy in ${MgB}_{2}$ : Interpretation of ${MgB}_{2}$ Raman spectra

Matteo Calandra and Francesco Mauri

Phys. Rev. B 71, 064501 – Published 1 February 2005

Abstract

We consider a model Hamiltonian fitted on the ab initio band structure to describe the electron-phonon coupling between the electronic $σ$ bands and the phonon $E_{2 g}$ mode in ${MgB}_{2}$ . The model allows for analytical calculations and numerical treatments using very large $k$ -point grids. We calculate the phonon self-energy of the $E_{2 g}$ mode along two high symmetry directions in the Brillouin zone. We demonstrate that the contribution of the $σ$ bands to the Raman linewidth (Landau damping) of the $E_{2 g}$ mode via the electron-phonon coupling is zero. As a consequence the large resonance seen in Raman experiments cannot be interpreted as originated from the $E_{2 g}$ mode at $Γ$ . We examine in details the effects of Fermi surface singularities in the phonon spectrum and linewidth and we determine the magnitude of finite temperature effects in the phonon self-energy. From our findings we suggest several possible effects which might be responsible for the ${MgB}_{2}$ Raman spectra.