  Fully gapped, spin singlet superconductors with antisymmetric spin-orbit
coupling in a Zeeman magnetic field provide a promising route to realize
superconducting states with non-Abelian topological order and therefore
fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical
cluster approximation to study the superconducting properties of a doped
two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a
Zeeman magnetic field. We generally find that the Rashba coupling has a
beneficial effect towards s-wave superconductivity. In the presence of a finite
Zeeman field, when superconductivity is suppressed by Pauli pair-breaking, the
Rashba coupling counteracts the spin imbalance created by the Zeeman field by
mixing the spins, and thus restores superconductivity at finite temperatures.
We show that this favorable effect of the spin-orbit coupling is traced to a
spin-flip driven enhancement of the amplitude for the propagation of a pair of
electrons in time-reversed states. Moreover, by inspecting the Fermi surface of
the interacting model, we show that for sufficiently large Rashba coupling and
Zeeman field, the superconducting state is expected to be topologically
non-trivial.
