  LaOBiS2-type materials have drawn much attention recently because of various
interesting physical properties, such as low-temperature superconductivity,
hidden spin polarization, and electrically tunable Dirac cones. However, it was
generally assumed that each LaOBiS2-type compound has a unique and specific
crystallographic structure (with a space group P4/nmm) separated from other
phases. Using first-principles total energy and stability calculations we
confirm that the previous assignment of the centrosymetric P4/nmm structure to
LaOBiS2 is incorrect as a phonon instability renders this structure impossible.
Furthermore, we find that the unstable structure is replaced by a family of
energetically closely spaced modifications (polytypes) differing by the layer
sequences and orientations. We find that the local Bi-S distortion leads to
three polytypes of LaOBiS2 with different stacking patterns of the distorted
BiS2 layers. The energy difference between the polytypes of LaOBiS2 is merely
~1 meV/u.c., indicating the possible coexistence of all polytypes in the real
sample and that the particular distribution of polytypes may be growth-induced.
The in-plane distortion can be suppressed by pressure, leading to a phase
transition from polytypes to the high-symmetry P4/nmm structure with a pressure
larger than 2.5 GPa. In addition, different choices of the intermediate atoms
(replacing La) or active atoms (BiS2) could also manifest different ground
state structures. One can thus tune the distortion and the ground state by
pressure or substituting covalence atoms in LaOBiS2-family.
