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 = ($π$, 0, 0) and several other \textbf{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.

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