Pairing Mechanism of Unconventional Superconductivity in Doped Kane-Mele Model

We study the pairing symmetry of a doped Kane-Mele model on a honeycomb lattice with on-site Coulomb interaction. The pairing instability of a Cooper pair is calculated on the basis of the linearized Eliashberg equation within the random phase approximation (RPA). When the magnitude of the spin-orbit coupling is weak, the even-frequency spin-singlet even-parity (ESE) pairing is dominant. On the other hand, with the increase in the magnitude of the spin orbit coupling, we show that the even-frequency spin-triplet odd-parity (ETO) f-wave pairing exceeds the ESE one. The ETO f-wave pairing is supported by the longitudinal spin fluctuation. Since the transverse spin fluctuation is strongly suppressed by spin-orbit coupling, the ETO f-wave pairing becomes dominant for a large magnitude of spin-orbit coupling.