Mixture of the nearest- and next-nearest-neighbor d plus id-wave pairings on the honeycomb lattice

Symmetry of superconducting pairing is one of the cardinal issues in superconductivity. In general, the nearest-neighbor and next-nearest-neighbor pairings cannot spontaneously mix with each other constrained by the distinct symmetry classification, for example the d(x2)-(y2) d (xy) -wave pairings in the square lattice. The honeycomb lattice provides a special platform to study the mixture of the nearest-neighbor and the next-nearest-neighbor pairing components due to its unique crystal structure. Here, using the variational quantum Monte Carlo simulations, we report a robust superconducting ground state with the intrinsic mixture of the nearest-neighbor and next-nearest-neighbor chiral d + id-wave pairings on the honeycomb lattice. We numerically identify that the two pairing channels promote each other. The proportion of the next-nearest-neighbor d + id component can be readily tuned by doping density and the short-range interactions. Our results provide the efficient ways to manipulate the real-space pairings.