Electric field gradients in s -, p -, and d -metal diborides and the effect of pressure on the band structure and T c in MgB 2

Results of full-potential linear muffin-tin orbital generalized gradient approximation calculations of the band structure and boron electric field gradients (EFG's) for the new medium-${T}_{c}$ superconductor ${\mathrm{MgB}}_{2}$ and related diborides $M{\mathrm{B}}_{2},$ $M=\mathrm{Be},$ Al, Sc, Ti, V, Cr, Mo, and Ta are reported. The boron EFG variations are found to be related to specific features of their band structure and particularly to the $M\ensuremath{-}\mathrm{B}$ hybridization. The strong charge anisotropy at the B site in ${\mathrm{MgB}}_{2}$ is completely defined by the valence electrons\char22{}a property which sets ${\mathrm{MgB}}_{2}$ apart from other diborides. The boron EFG in ${\mathrm{MgB}}_{2}$ is weakly dependent on applied pressure: the B p-electron anisotropy increases with pressure, but it is partly compensated by the increase of core charge asymmetry. The concentration of holes in bonding \ensuremath{\sigma} bands is found to decrease slightly from 0.067 to 0.062 holes/B under a pressure of 10 GPa. Despite a small decrease of ${N(E}_{F}),$ the Hopfield parameter increases with pressure and we believe that the main reason for the reduction under pressure of the superconducting transition temperature ${T}_{c}$ is the strong pressure dependence of phonon frequencies, which is sufficient to compensate for the electronic effects.