  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.
