Cooperative enhancement of superconducting pairing at quarter filling by electron-electron and electron-phonon interactions

Unbiased numerical calculations within two-dimensional Hubbard models have found no evidence for long-range superconducting order. This suggests that repulsive interactions between electrons alone are not sufficient to realize superconductivity and other interactions are required. The most likely candidate is the electron-phonon interaction. However, existing theories of superconductivity emphasize either electron-electron or electron-phonon interactions, each of which tends to cancel the effect of the other. We present direct evidence from quantum Monte Carlo calculations of cooperative, as opposed to competing, effects of electron-electron and electron-phonon interactions within the frustrated Hubbard Hamiltonian, uniquely at the band-filling of one-quarter[1]. Bond-coupled phonons and the onsite Hubbard U cooperatively
reinforce d-wave superconducting pair-pair correlations at this filling while competing with one another at all other densities. Our work further gives new insight into how intertwined charge-order and superconductivity appear in real materials.

[1] R.T. Clay and D. Roy, Phys. Rev. Research 2, 023006 (2020)