Superconductivity due to cooperation of electron-electron and electron-phonon interactions at quarter filling

Existing theories of superconductivity emphasize either electron-electron or electron-phonon interaction, each of which tends to cancel the effect of the other. We present direct evidence from unbiased numerical calculations of cooperative, as opposed to competing, effects of electron-electron and electron-phonon interactions within the frustrated Hubbard Hamiltonian with bond-coupled phonons, uniquely at the band filling of one-quarter. The two interactions cooperatively reinforce d-wave superconducting pair-pair correlations at this filling while competing with one another at all other densities. Our work gives insight into how intertwined charge order and superconductivity appear in real materials.