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, 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. 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–d + id superconducting electron pairing symmetry, and that such nearest-neighbor attractive Coulomb interactions significantly enhance the effective long-range pairing correlation function of chiral NN–d + id wave. From this perspective, it is evident that electronphonon coupling positively contributes to the superconductivity of the system.
Subsequently, we explore how the twist angle affects the superconducting state. The flat-band structure conducted 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–d + id wave increases substantially. Conversely, as the twist angle exceeds 1.08°, the effective correlation function of the chiral NN–d + id wave exhibits a tendency of decline. These results suggest that further reduction in the twist angle may lead to higher superconducting transition temperatures in twisted bilayer graphene system.
Ultimately, 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–d + id wave. Through this series of investigations, our numerical findings not only contribute to a more comprehensive understanding of strongly correlated systems such as twisted bilayer graphene, but also offer guidance for identifying twist-angle systems with potentially higher superconducting transition temperatures.