Possible $f$-wave pairing in the low-doping regime of monolayer MoS$_2$

We investigate the possible superconducting pairing state in a theoretical model for monolayer-MoS$_2$ by using the temperature-flow functional renormalization group (fRG). In the low doping regime, the dominant instability lies in the odd-parity pairing channel. It has a $f$-wave pairing structure within the $D_{3h}$ point-group symmetry. We also compute the fRG phase diagram below the van-Hove filling. In the superconducting regime, the critical temperature grows with increasing doping, comparable to the experiments. We demonstrate that the pairing is driven by ferromagnetic fluctuations. When the band filling is close to the van-Hove filling, the system favors a ferromagnetic state.