s-Wave Superconductivity Phase Diagram in the Inhomogeneous Two-Dimensional Attractive Hubbard Model

We study s-wave superconductivity in the 2-D square lattice attractive Hubbard Hamiltonian for inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns with on-site electron interaction $U_i$ taking on two values, $0$ and $-U/(1-f)$ ($f$ the non-interacting sites concentration) as a function of electron density per site $n$ as $f$ varies. Inhomogeneity can result in a larger average pairing amplitude at $T=0$ and also a higher superconducting $T_c$, relative to a uniform system. Superconductivity can also vanish due to charge ordered phase formation. $T_c$ enhancement due to inhomogeneity is robust as long as $n<2(1-f)$ regardless of the pattern. Also, for certain inhomogeneous patterns, when $n=2(1-f)$, raising temperature works against the stability of existing charge ordered phases for large $f$ and as a result, enhances $T_c$.