Effects of stoichiometric doping in superconducting Bi-O-S compounds

Newly discovered Bi-O-S compounds remain an enigma in attempts to understand their electronic properties. A recent study of Bi$_{4}$O$_{4}$S$_{3}$ has shown it to be a mixture of two phases, Bi$_{2}$OS$_{2}$ and Bi$_{3}$O$_{2}$S$_{3}$, the latter being superconducting [W. A. Phelan et al., J. Am. Chem. Soc. 135, 5372 (2013)]. Using density functional theory, we explore the electronic structure of both the phases and the effect of the introduction of stacking faults. Our results demonstrate that the S$_{2}$ layers dope the bismuth-sulphur bands. The bands at the Fermi level are of clear two-dimensional character. One band manifold is confined to the two adjacent, square-lattice bismuth-sulphur planes, a second manifold is confined to the square lattice of sulphur dimers. We show that the introduction of defects in the stacking does not influence the electronic structure. Finally, we also show that spin-orbit coupling does not have any significant effect on the states close to the Fermi level at the energy scale considered.