We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the superconductor $\mathrm{MgB}{}_2$ and the isostructural $\mathrm{AlB}{}_2$ within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. Complete phonon dispersion curves and Eliashberg functions ${\alpha }^{2}F$ are calculated for both systems. The main differences are related to high frequency in-plane boron vibrations, which are strongly softened in $\mathrm{MgB}{}_2$ and exhibit an exceptionally strong electron-phonon coupling. We also report on Raman measurements, which support the theoretical findings. Implications for the superconducting transition temperature are briefly discussed.

• Received 15 March 2001

DOI:https://doi.org/10.1103/PhysRevLett.86.5771