-wave Superconductivity in Weakly Repulsive 2D Hubbard Model with Zeeman Splitting and Weak Rashba Spin-orbit Coupling*

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by the Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel depends on the filling fraction n of the system, and the momentum dependence of the order parameter can thus be changed by tuning n. The filling fraction also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to chiral p_x±ip_y type states for out-of-plane fields, to nodal p-wave type states for purely in-plane fields.