  Many theoretical approaches find d-wave superconductivity in the prototypical
one-band Hubbard model for high-temperature superconductors. At strong-coupling
(U > W, where U is the on-site repulsion and W=8t the bandwidth) pairing is
controlled by the exchange energy J=4t^2/U. One may then surmise, ignoring
retardation effects, that near-neighbor Coulomb repulsion V will destroy
superconductivity when it becomes larger than J, a condition that is easily
satisfied in cuprates for example. Using Cellular Dynamical Mean-Field theory
with an exact diagonalization solver for the extended Hubbard model, we show
that pairing, at strong coupling, is preserved even when V>>J, as long as
V<U/2. While at weak coupling V always reduces the spin fluctuations and hence
d-wave pairing, at strong coupling, in the underdoped regime, the increase of
J=4t^2/(U-V) caused by V increases binding at low frequency while the
pair-breaking effect of V is pushed to high frequency. These two effects
compensate in the underdoped regime, in the presence of a pseudogap. While the
pseudogap competes with superconductivity, the proximity to the Mott transition
that leads to the pseudogap, and retardation effects, protect d-wave
superconductivity from V.
