  We study the effects of static nonlocal Coulomb interactions in layered
conventional superconductors and show that they generically suppress
superconductivity and reduce the critical temperature. Although the nonlocal
Coulomb interaction leads to a significant structure in the superconducting gap
function, we find that most properties can be effectively described by means of
an appropriately revised local Coulomb pseudopotential $\tilde{\mu}_C^*$, which
is larger than the commonly adopted retarded Tolmachev-Morel-Anderson
pseudopotential $\mu^*_C$. To understand this, we analyze the Bethe-Salpeter
equation describing the screening of Coulomb interaction in the superconducting
state and obtain an expression for $\tilde{\mu}_C^*$, which is valid in the
presence of nonlocal Coulomb interactions. This analysis also reveals how the
structure of the nonlocal Coulomb interaction weakens the screening effects
from high-energy pair fluctuations and therefore yields larger values of the
pseudopotential. Our findings are especially important for layered conventional
superconductors with small Fermi energies and can be easily taken into account
ab initio studies.
