We explore magnetic correlations and superconducting pairing near higher-order Van Hove singularities in an extended Hubbard model on honecycomb lattice incorporating third-nearest-neighbor hopping \ (t'' \). Using quantum Monte Carlo methods, we identify a crossover between ferromagnetic and antiferromagnetic fluctuations near higher-order Van Hove singularities filling, where \ (t'' \) enhances ferromagnetic correlations below while suppressing antiferromagnetic fluctuations toward half-filling. At low doping, \ (fₙ \) -wave pairing dominates, amplified by higher-order Van Hove singularities-induced divergent density of states. Remarkably, despite general suppression of \ (fₙ \) -wave pairing by increasing next-nearest neighbor hopping \ (t' \) and \ (t'' \), a critical \ (t'' = 0. 15 \) triggers anomalous enhancement via higher-order Van Hove singularities renormalization at a fix t'. The nearest-neighbor Coulomb interactions \ (V \) suppress superconducting correlation, which exhibiting sign-independent suppression proportional to \ (|V| \). These results highlight the interplay of higher-order Van Hove singularities-driven electronic structure, magnetic fluctuations, and pairing symmetry competition in electron correlated systems.
Wei et al. (Thu,) studied this question.