Mechanism for unconventional superconductivity in the hole-doped Rashba-Hubbard model

Motivated by the recent resurgence of interest in topological superconductivity, we study in this paper superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within a weak-coupling approach based on the random phase approximation, we compute the spin-fluctuation mediated paring interactions as a function of spin-orbit coupling and hole doping. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that for a broad doping region in between these two van Hove fillings the spin fluctuations exhibit a strong ferromagnetic contribution. Because of these ferromagnetic fluctuations, the triplet $f$-wave pairing channel is dominant within this filling region, resulting in a topologically nontrival phase. We discuss possible experimental realizations of this phase in heavy-fermion hybrid structures.