  We investigate parity-mixing superconductivity in the two-dimensional Hubbard
model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field
Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet
$p$-wave character is found in a wide range of doping. The singlet component
decreases with the amplitude of the Rashba spin-orbit coupling, whereas the
triplet component increases, but both disappear at about 20\% doping. The
effect of a Zeeman field is also investigated; it tends to suppress both types
of superconductivity, but induces nontrivial topological properties: the
computed bulk Chern number is nonzero in the mixed superconductivity phase, at
least in the underdoped region. A strong suppression of the excitation gap
occurs slightly after optimal doping; this might be the sign of a topological
transition within the superconducting dome.
