Third-nearest-neighbor-hopping-driven competition between chiral p+ ip and triplet f-wave pairing in a doped honeycomb-lattice Hubbard model

We study how third-nearest-neighbor hopping [Formula: see text] reshapes pairing selection in the weak-coupling honeycomb-lattice Hubbard model at low filling. Within the random-phase approximation, we track the evolution of the band structure, Fermi surface, bare susceptibility, and eigenvalue spectrum of the linearized gap equation for fixed nearest-neighbor hopping [Formula: see text], next-nearest-neighbor hopping [Formula: see text]. At filling [Formula: see text], for small [Formula: see text], the leading instability is a nearly degenerate [Formula: see text] doublet that combines into a chiral [Formula: see text] state. As [Formula: see text] increases, the low-energy dispersion around the [Formula: see text] point is reconstructed, the low-momentum fluctuation pattern favoring chiral [Formula: see text]-wave pairing is weakened, and the triplet [Formula: see text]-wave channel becomes progressively more competitive. Near [Formula: see text], the triplet [Formula: see text]-wave eigenvalue slightly exceeds that of the chiral [Formula: see text] channel, signaling a change in the leading pairing instability. Further, the [Formula: see text]-[Formula: see text] phase diagram shows that the [Formula: see text]-wave region first appears on the low-filling side and then expands toward larger filling as [Formula: see text] increases. These results clarify how long-range hopping controls pairing competition in doped honeycomb systems and provide a weak-coupling route toward stabilizing higher-angular-momentum triplet superconductivity through band-structure engineering.