  The band structure of cubic inverse perovskites, Ca_3PbO and its family, are
investigated with the first-principles method. A close observation of the band
structure reveals that six equivalent Dirac electrons with a very small mass
exist on the line connecting the Gamma- and X-points, and at the symmetrically
equivalent points in the Brillouin zone. The discovered Dirac electrons are
three-dimensional and remarkably located exactly at the Fermi energy. A
tight-binding model describing the low-energy band structure is also
constructed and used to discuss the origin of the Dirac electrons in this
material. Materials related to Ca_3PbO are also studied, and some design
principles for the Dirac electrons in this series of materials are proposed.
