A constrained path quantum Monte Carlo simulation is performed to investigate the superconducting pairing correlation in doped staggered-flux Hubbard model on a square lattice, which is an interesting platform to host Dirac fermions. For various electron fillings and interaction strengths, the $d_{x y}$ pairing dominates over other pairing forms since its long-range correlation is larger over mostly distances. We deepen our study by including the nearest-neighbor interaction $V$ and found the $d_{x y}$ pairing correlation is slightly suppressed by increasing $V$ .

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