  We study the spin-fluctuation-mediated superconducting pairing gap in a
weak-coupling approach to the Hubbard model for a two dimensional square
lattice in the paramagnetic state. Performing a comprehensive theoretical study
of the phase diagram as a function of filling, we find that the superconducting
gap exhibits transitions from p-wave at very low electron fillings to
d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous
reports. At intermediate filling levels, different gap symmetries appear as a
consequence of the changes in the Fermi surface topology and the associated
structure of the spin susceptibility. In particular, the vicinity of a van Hove
singularity in the electronic structure close to the Fermi level has important
consequences for the gap structure in favoring the otherwise sub-dominant
triplet solution over the singlet d-wave solution. By solving the full gap
equation, we find that the energetically favorable triplet solutions are chiral
and break time reversal symmetry. Finally, we also calculate the detailed
angular gap structure of the quasi-particle spectrum, and show how
spin-fluctuation-mediated pairing leads to significant deviations from the
first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral
triplet gap solution.

Superconductivity