Band structure of the superconducting MgB$_2$ compound and modeling of related ternary systems

Band structure of a novel superconductor-magnesium diboride is studied by the self-consistent FP-LMTO method. Density of states near the Fermi level of MgB$_2$ and its electronic properties are governed by the metal-like boron $2p$ orbitals in the planar network of boron atoms. The modification of the band structure of MgB$_2$ upon doping the boron (with Be, C, N, and O substitutional impurities) and the magnesium (with Be, Ca, Li, and Na substitutional impurities) sublattices or upon the introduction of structural vacancies (boron nonstoichiomety) is analyzed. The electronic structures of MgB$_2$ and hypothetical CaB$_2$ are also studied as functions of pressure.