Charge and spin fluctuations in superconductors with intersublattice and interorbital interactions

Multiband superconductors have featured one of the main challenges to achieve a comprehensive understanding of unconventional superconductivity. Here, the multiband character is studied separately as orbital and sublattice degrees of freedom, as they have different effects for the superconducting and magnetic or charge orders. We build on the framework of the matrix random-phase approximation (RPA), which accounts for the RPA Feynman diagrams and also vertex corrections, to treat the electron-electron interactions in an off-site degenerate Hubbard model. As a result, systems without a sublattice degree of freedom tend to be dominated by spin fluctuations, while systems with multiple sublattice sites and orbitals have the charge fluctuations favored. Finally, we explicitly demonstrate that the known suppression of the superconducting pairing strength $\lambda$ by spin fluctuations from repulsive interactions at zero momentum transfer $\boldsymbol{q}$ is countered by the finite-$\boldsymbol{q}$ pairing, which always improves $\lambda$.