Three-Dimensional Dirac Electrons at the Fermi Energy in Cubic Inverse Perovskites: Ca3PbO and Its Family

The band structure of cubic inverse perovskites, Ca 3 PbO 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 3 PbO are also studied, and some design principles for the Dirac electrons in this series of materials are proposed.