Energy bandstructures of MgB2 and the related compounds

Energy band structures are calculated for the new superconductor MgB2 and the related compounds by using the LDA and an FLAPW method. It is found that the strong three dimensional network in low-lying π bands brings about two dimensional σ holes in MgB2, which should be responsible for the superconductivity. The de Haas-van Alphen frequencies and the cyclotron masses are obtained for the Fermi surfaces. The σ hole is not found in LiBC due to the less three dimensional network. MgB2C2 is found a semiconductor, but the top of the valence bands are similar to the σ bands in MgB2. The total energy calculations are also performed for Mg1−xAlxB2 to investigate the structural phase instability, experimentally observed around x =10%. PACS codes:71.18.+y, 71.20.-b, 74.25, 74-70.-b