  The two-dimensional (2D) Hubbard model is widely believed to contain the key
ingredients of high-temperature superconductivity in cuprate materials. Here,
we report a constrained path quantum Monte Carlo (CPQMC) study of the
square-lattice extended Hubbard model with on-site Coulomb repulsion U and
nearest-neighbor (NN) electron attraction V. Upon doping $\delta$= 0.125, we
find that the NN electron attraction V can notably drive an exotic spin-triplet
(p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations
with the increase of V. But in the intermediate coupling regime, the
$d_{x^2-y^2}$-wave (d-wave) does not significantly increase with the increase
of V, indicating that the d-wave is not affected by V in strongly correlated
system. Besides the pairing phase, a spin density wave (SDW) only exists near
the half-filling in the particle-hole channel, and doping disrupts the
formation of SDW order. Especially, the NN electron attraction V has no
significant effect on SDW, reflecting the consistent relationship between
d-wave SC and spin correlation. Moreover, as doping increases, the dominant
region of p-wave also expands, further suppressing the presence of d-wave,
which may help explain the disappearance of d-wave SC in overdoped cuprate
superconductors. We also find the d-wave exhibits a singular nonzero (near
point ($2{\pi}/3, {\pi}$)) condensation structure in momentum space, resulting
in a different staggered behavior in the x and y direction with distance in
real space. On the contrary, the p-wave condensed at zero momentum, and the
p-wave correlation exhibits exponential decay in real space. Our work suggests
the p-wave SC region can be induced and further broadened by the NN electron
attraction V, offering a feasible mechanism to realize p-wave superconductivity
in realistic cuprate materials.
