Competing superconducting phases in the interacting two-dimensional electron gas with strong Rashba spin-orbit coupling

In this work, we study interacting electrons on a square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consider the repulsive onsite Hubbard and nearest-neighbor Coulomb interactions, the socalled extended Hubbard model. To examine the superconducting instability, we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings and found that while the d(xy) and d(x2-y2) symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instabilities. The possibility of topological superconductivity and triplet pairing is also discussed.