Electronic fine structure in the nickel carbide superconductor Th$_{2}$NiC$_{2}$

The recently reported nickel carbide superconductor, body centered tetragonal $I4/mmm$ Th$_2$NiC$_2$ with T$_c$ = 8.5 K increasing to 11.2 K upon alloying Th with Sc, is found to have very fine structure in its electronic spectrum, according to density functional based first principles calculations. The filled Ni 3d band complex is hybridized with C $2p$ and Th character to and through the Fermi level ($E_f$), and a sharply structured density of states arises only when spin-orbit coupling is included, which splits a zone-center degeneracy leaving a very flat band edge lying at the Fermi level. The flat part of the band corresponds to an effective mass $m^*_{z} rightarrow infty$ with large and negative $m^*_{x}=m^*_{y}$. Although the region over which the effective mass characterization applies is less than 1% of the zone volume, it yet supplies of the order of half the states at (or just above) the Fermi level. The observed increase of T$_c$ by hole-doping is accounted for if the reference as-synthesized sample is minutely hole-doped, which decreases the Fermi level density of states and will provide some stabilization. In this scenario, electron doping will increase the Fermi level density of states and the superconducting critical temperature. Vibrational properties are presented, and enough coupling to the C-Ni-C stretch mode at 70 meV is obtained to imply that superconductivity is electron-phonon mediated.