2 carrier density electron-phonon coupling cannot be too strong. This leads us to the conclusion that the superconduc- tivity in the hole-doped BiOCu$_{1}$$_{−}$$_{y}$S must be unconven- tional, and probably magnetically mediated, although it is not clear yet what particular pairing symmetry can be generated in this material. One can question the validity of the virtual crystal ap- proximation, given that holes are introduced not through  0  1  2  3  4  5  6 -1 -0.5  0  0.5  1  1.5  2 N(E), states/eV f.u. Energy, eV total Cu Bi O S interst. -1  0  1  2  3  4  0  0.05  0.1  0.15  0.2  0.25  0.3 Total energy, meV/Cu Magnetic moment, $_{B}$/Cu  0  10  20  0 0.2 FIG. 4: Fixed spin moment calculations for BiOCu 1$_{−}$ y S for y = 0 . 2. The self-consistent solution is indicated by the ar- row. Note that the energy is essentially independent of the magnetic moment up to the half-metallic magnetization of y µ$_{B}$ /Cu. The inset shows a linear growth of the total energy when magnetization exceeds the half-metal limit. FIG. 3: (color online) Left panel: The Fermi surface of BiOCu 1$_{−}$ y S at E$_{F}$ 120 meV below the gap, where a sharp peak in DOS starts. Note a cross-shaped pocket emerging along the Z$_{−}$A direction, responsible for this peak. For com- parison, in the right panel the Fermi surface at E$_{F}$ = 150 meV ( y ∼ 0 . 15) is shown, where the peak is already fully de- veloped. Both Fermi surfaces are colored according the the absolute value of the Fermi velocity using the same scale (blue is zero). FIG. 2: Density of states of BiOCuS near the Fermi level. Note a peak right below the gap, and the leading contribution of the Cu states below, and the interstitial states above the band gap. (color online) substitution, but through Cu vacancies. To verify that, I have performed supercell calculations using four for- mula units with one vacancy, that is to say, Bi$_{4}$O$_{4}$Cu$_{3}$S$_{4}$ , corresponding to y = 0 . 25 . The calculations converged to a ferromagnetic state with M = 0 . 2 µ$_{B}$ per formula unit (0.8 µ$_{B}$ per supercell), again slightly below the half- metallic limit of 0.25 µ$_{B}$, thus confirming the validity of the virtual crystal calculations. Interestingly, the magne- tization was quite delocalized, with Cu ions carrying 0.1 – 0.13 µ$_{B}$, and the rest of the magnetic moment distributed among the sulfur ions and in the interstitial region. I thank Dirk van der Marel for stimulating discussions related to this work, and Peter Blaha for a technical con- sulation. I also acknowledge funding from the Office of Naval Research. GGA calculations also yield infinite susceptibility $^{9}$. As in Pd, or, for that matter, in Fe pnictides, fluctuations beyond the mean-field level should suppress magnetiza- tion and reduce the susceptibility to a large, but finite value. But, again as in Pd, strong spin fluctuations are bound to destroy any conventional s-wave superconduc- tivity, particularly given that with this relatively modest 4 H. Hiramatsu, H. Yanagi, T. Kamiya, K. Ueda, M. Hirano and H. Hosono Chem., Mater., 20 , 326 (2008) 5 The full-potential LAPW method, as implemented in the WIEN2k packege, has been used for all calculations. Up to 840 inequivalent k-points have been utilized to achieved the self-consistency, with the energy convergency better then 1 A. Ubaldini, E. Giannini, C. Senatore, D. van der Marel , arXiv:0911.5305 (unpublished). 2 A. Pal, H. Kishan and V.P.S. Awana, arXiv:0912.0991 (un- published) 3 I. R. Shein and A. L. Ivanovskii, Solid State Communica- tions, 150 , 640 (2010)