Enhancement of superconductivity by local inhomogeneities

We study the effect of inhomogeneity of the pairing interaction or the background potential on the superconducting transition temperature, $T_c$. In the weak coupling BCS regime, we find that inhomogeneity, which is incommensurate with the Fermi surface nesting vectors, enhances $T_c$ relative to its value for the uniform system. For a fixed modulation strength we find that the highest $T_c$ is reached when the characteristic modulation length scale is of the order of the superconducting coherence length.