Electron-phonon coupling and superconductivity in MgB2 and related diborides

A brief review of the electron-phonon coupling scenario for the superconductor MgB2 and related diborides on the basis of ab initio density-functional calculations is presented. We show results for phonon dispersions and electron-phonon spectral functions and discuss their implications for superconducting properties in the isotropic limit. The hydrostatic pressure derivative of T-c for MgB2 is found to be consistent with experiment. Calculations for AlB2 and a hypothetical superstructure MgAlB4 are performed to study the doping dependence of the electron-phonon coupling. Differences to transit ion-metal diborides are investigated for NbB2 and TiB2. We also include a brief discussion of limitations and extensions of the simple isotropic picture.