  We show how strongly interacting two-dimensional Dirac fermions can be
realized with ultracold atoms in a two-dimensional optical square lattice with
an experimentally realistic, inherent gauge field, which breaks time-reversal
and inversion symmetries. We find remarkable phenomena in a temperature range
around a tenth of the Fermi-temperature, accessible with present experimental
techniques: at zero chemical potential, besides a conventional s-wave
superconducting phase, unconventional superconductivity with non-local bond
pairing arises. In a temperature versus doping phase diagram, the
unconventional superconducting phase exhibits a dome structure, reminiscent of
the phase diagram for high-temperature superconductors and heavy fermions.
