  Recent ARPES measurements [Phys. Rev. B 92, 041113 (2015)] have confirmed the
one-dimensional character of the electronic structure of CeO0.5F0.5BiS2, a
representative of BiS2-based superconductors. In addition, several members of
this family present sizable increase in the superconducting transition
temperature Tc under application of hydrostatic pressure. Motivated by these
two results, we propose a one-dimensional three-orbital model, whose kinetic
energy part, obtained through ab initio calculations, is supplemented by
pair-scattering terms, which are treated at the mean-field level. We solve the
gap equations self-consistently and then systematically probe which combination
of pair-scattering terms gives results consistent with experiment, namely, a
superconducting dome with a maximum Tc at the right chemical potential and a
sizable increase in Tc when the magnitude of the hoppings is increased. For
these constraints to be satisfied multi-gap superconductivity is required, in
agreement with experiments, and one of the hoppings has a dominant influence
over the increase of Tc with pressure.
