Density matrix renormalization group study of superconducting pairing near the quarter-filled Wigner crystal

Charge ordering is often found in the phase diagram of unconventional superconductors in close proximity to the superconducting state. This has led to the suggestion that fluctuations of charge order can mediate superconducting pairing. While several mechanisms can lead to charge order, one common mechanism is the long-range Coulomb interaction, resulting in a Wigner crystal charge ordered state. For an electron density of 0.5 per site, we investigate the extended Hubbard model on the two-dimensional square lattice using exact diagonalization and density matrix renormalization group methods. Our results show that the strength of pairing decreases with the nearest-neighbor Coulomb interaction strength $V$ and remains weaker than the tendency of pairing for noninteracting electrons.