Electronic structure of superconducting layered zirconium and hafnium nitride

Abstract

The electronic energy-band structures for \ensuremath{\beta}-ZrNCl and \ensuremath{\beta}-HfNCl, which can be superconducting by intercalation, have been calculated by using the scalar-relativistic full-potential linearized augmented-plane-wave method within the local-density approximation. For \ensuremath{\beta}-ZrNCl, we have calculated the electronic structure for the four proposed crystal structures, and obtained two kinds of qualitatively different energy bands. For the first two structures, the calculations show that this compound is a band insulator with a gap of \ensuremath{\sim}0.2 eV, which is significantly smaller than the experimental value. For the last two structures, this band gap is increased to \ensuremath{\sim}1.6 and \ensuremath{\sim}0.8 eV, which is closer to the experiment. A comparison between other experimental data and the calculated density of states also supports the crystal structure of the recent neutron-diffraction experiment. A tight-binding analysis has revealed that direct $d\ensuremath{-}d$ hopping is important for the gap formation of the mother material. We have compared the experimental ${T}_{c}$ gap calculated band gap, and density of states for several intercalation-derived superconductors, and found some empirical trends.