We employ a large-scale, unbiased constrained-path quantum Monte Carlo method to systematically simulate the effective two-orbital Hubbard model for twisted bilayer graphene in order to gain deeper insight into the relationship between correlated states and the superconducting pairing mechanism in twisted bilayer graphene, as well as the influence of the twist angle on superconductivity. Initially, we investigate the modulation of superconductivity by nearest-neighbor attractive Coulomb interactions, demonstrating that electron-phonon coupling plays a significant role in the system. Our numerical results reveal that the superconducting state is dominated by chiral NN-\mathrmd+\mathrmid superconducting electron pairing symmetry, and that such nearest-neighbor attractive Coulomb interactions significantly enhance the effective long-range pairing correlation function of chiral NN-\mathrmd+\mathrmid wave. From this perspective, it is evident that the electron-phonon coupling positively contributes to the superconductivity of the system.

Then, we explore how the twist angle affects the superconducting state. The flat-band structure caused by hopping anisotropy reflects the different twist angles of the system. Our results show that as the twist angle deviates downward from 1.08°, the effective pairing correlation function of the chiral NN-\mathrmd+\mathrmid wave increases substantially. Conversely, as the twist angle exceeds 1.08°, the effective correlation function of the chiral NN-\mathrmd+\mathrmid wave exhibits a tendency of decline. These results suggest that further reduction of the twist angle may lead to higher superconducting transition temperature in twisted bilayer graphene system.

Finally, we analyze how nearest-neighbor attractive Coulomb interactions and flat-band structures influence superconductivity from the standpoint of magnetic properties. The observed enhancement of the spin structure factor near the Γ point in the Brillouin zone indicates that enhanced antiferromagnetic correlations are essential for enhancing the superconducting transition temperature and for stabilizing chiral NN-\mathrmd+\mathrmid wave. Through these investigations, our numerical findings not only contribute to a more comprehensive understanding of strongly correlated systems such as twisted bilayer graphene, but also provide guidance for identifying twist-angle systems with potentially higher superconducting transition temperatures.