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Recent angle-resolved spectroscopy in BiS$_2$-based superconductors hasindicated that the superconducting gap amplitude possesses remarkableanisotropy and/or a sign change on a small Fermi pocket around $X$ point. Itimplies a possibility of an unconventional pairing state. Here we study the gapanisotropy in superconductivity mediated by inherent charge/quadrupolefluctuations in an extended Hubbard model, which includes inter-siteinteraction between Bi and S atoms. The first-principles downfolded bandstructure is composed of Bi $6p_x/p_y$ and S $3p_x/p_y$ orbitals on a BiS$_2$single layer. Evaluating the linearized gap equation, we find that the ferroiccharge/quadrupole fluctuation driven by the inter-site interaction leads to afully-gapped $d_{x^2-y^2}$-wave pairing state, in which the gap amplitude hassizable anisotropy on the Fermi surface.

Charge/quadrupole fluctuations and gap anisotropy in BiS$_2$-based superconductors