Resilience of d-wave superconductivity to nearest-neighbor repulsion

Many theoretical approaches find $d$-wave superconductivity in the one-band Hubbard model for high-temperature superconductors. At strong-coupling ($U\geq W$, 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 {\it at strong coupling} is preserved, even when $V\gg J$, as long as $V \la U/2$. 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 $V$. PRB 87, 075123 (2013)