Vacancies, disorder-induced smearing of the electronic structure, and its implications for the superconductivity of anti-perovskite MgC$_{0.93}$Ni$_{2.85}$
The anti-perovskite superconductor MgC$_{0.93}$Ni$_{2.85}$ was studied using high-resolution x-ray Compton scattering combined with electronic structure calculations. Compton scattering measurements were used to determine experimentally a Fermi surface that showed good agreement with that of our supercell calculations, establishing the presence of the predicted hole and electron Fermi surface sheets. Our calculations indicate that the Fermi surface is smeared by the disorder due to the presence of vacancies on the C and Ni sites, but does not drastically change shape. The 20\% reduction in the Fermi level density-of-states would lead to a significant ($\sim 70\%$) suppression of the superconducting $T_c$ for pair-forming electron-phonon coupling. However, we ascribe the observed much smaller $T_c$ reduction at our composition (compared to the stoichiometric compound) to the suppression of pair-breaking spin fluctuations.