Phonon dispersion and electron-phonon coupling in MgB₂ and AlB₂

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We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the superconductor MgB₂ and the isostructural AlB₂ within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. Complete phonon dispersion curves and Eliashberg functions α²F are calculated for both systems. We also report on Raman measurements, which support the theoretical findings. The calculated generalized density-of-states for MgB₂ is in excellent agreement with recent neutron-scattering experiments. The main differences in the calculated phonon spectra and α²F are related to high frequency in-plane boron vibrations. As compared to AlB₂, they are strongly softened in MgB₂ and exhibit an exceptionally strong coupling to electronic states at the Fermi energy. The total coupling constants are λMgB₂=0.73 and λAlB₂=0.43. Implications for the superconducting transition temperature are briefly discussed.