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Electronic structure and the shape of the Fermi surface are known to be offundamental importance for the superconducting instability in real materials.We demonstrate that such an instability may be explored by static Cooper pairsusceptibility renormalized by pairing interaction and present an efficientmethod of its evaluation using Wannier orbitals derived from ab initiocalculation. As an example, this approach is used to search for anunconventional superconducting phase of the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) type in a heavy-fermion compound CeCoIn$_5$ and an iron-basedsuperconductor FeSe. The results suggest that the FFLO superconducting phaseoccurs at finite magnetic field in both materials.

The ab initio study of unconventional superconductivity in CeCoIn$_{5}$ and FeSe