Disorder-dependent superconducting pairing symmetry in doped graphene

Disorder and doping have profound effects on the intrinsic physical mechanisms of superconductivity. In this paper, we employed the determinant quantum Monte Carlo method to investigate the symmetry-allowed superconducting orders on the two-dimensional honeycomb lattice within the Hubbard model, using doped graphene as the carrier, focusing their response to bond disorder. Specifically, we calculated the pairing susceptibility and effective pairing interactions for the $d+id$ wave and extended $s$-wave pairings for different electron densities and disorder strengths. Our calculations show that at high electron densities, increased disorder strength may lead to a transform from $d+id$ wave dominance to extended $s$ wave dominance. However, at lower electron densities, neither of the two superconducting pairings appears under larger disorder strength. Our calculations may contribute to a further understanding of the superconducting behavior in doped materials affected by disorder.