Electronic structures of antiperovskite superconductors $\mathrm{Mg}X{\mathrm{Ni}}_3$ $(X=\mathrm{B},$ C, and N)

We have investigated electronic structures of a newly discovered antiperovskite superconductor ${\mathrm{MgCNi}}_3$ and related compounds ${\mathrm{MgBNi}}_3$ and ${\mathrm{MgNNi}}_3.$ In ${\mathrm{MgCNi}}_3,$ a peak of very narrow and high density of states is located just below the Fermi level, which corresponds to the ${\pi }^{*}$ antibonding state of Ni $3d$ and C $2p$ but with the predominant Ni $3d$ character. The prominent nesting feature is observed in the $\Gamma$-centered electron Fermi surface of an octahedron-cage-like shape that originates from the 19th band. The estimated superconducting parameters are in reasonable agreement with experiment, suggesting that the superconductivity in ${\mathrm{MgCNi}}_3$ is described properly by the conventional BCS phonon mechanism.