Structural and Electronic Properties of the 2D Superconductor CuS with 1   1/3-valent Copper
  We present first principle calculations of the structural and electronic properties of the CuS covellite material. Symmetry-lowering structural transition is well reproduced. However, the microscopic origin of the transition is unclear. The calculations firmly establish that the so far controversial Cu valency in this compound is 1.33. We also argue that recently reported high-temperature superconductivity in CuS is unlikely to occur in the stoichiometric defect-free material, since the determined Cu valency is too close to 1 to ensure proximity to a Mott-Hubbard state and superexchange spin fluctuations of considerable strength. On the other hand, one can imagine a related system with more holes per Cu in the same structural motif ($e.g.$, due to defects or O impurities) in which case combination of superexchange and an enlarged compared to CuS Fermi surface may lead to unconventional superconductivity, similar to HTSC cuprates, but, unlike them, of an $f$-wave symmetry. 
I. I. Mazin
cond-mat.mtrl-sci cond-mat.supr-con