Strong bilayer coupling induced by the symmetry breaking in the monoclinic phase of BiS${}_2$-based superconductors

We perform first-principles band structure calculations for the tetragonal and monoclinic structures of LaO${}_{0.5}$F${}_{0.5}$BiS${}_2$. We find that the Bi $6p_{x,y}$ bands on two BiS${}_2$ layers exhibit a sizable splitting at the X = ($\pi$, 0, 0) and several other $\mathbf{\text{k}}$-points for the monoclinic structure. We show that this feature originates from the inter-BiS${}_2$ layer coupling strongly enhanced by the symmetry breaking of the crystal structure. The Fermi surface also shows a large splitting and becomes anisotropic with respect to the $k_x$ and $k_y$ directions in the monoclinic structure, whereas it remains almost flat with respect to the $k_z$ direction.