  We study the attractive fermionic Hubbard model on a honeycomb lattice using
determinantal quantum Monte Carlo simulations. By increasing the interaction
strength U (relative to the hopping parameter t) at half-filling and zero
temperature, the system undergoes a quantum phase transition at 5.0 < U_c/t <
5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior
and density order. Doping away from half-filling, and increasing the
interaction strength at finite but low temperature T, the system always appears
to be a superfluid exhibiting a crossover between a BCS and a molecular regime.
These different regimes are analyzed by studying the spectral function. The
formation of pairs and the emergence of phase coherence throughout the sample
are studied as U is increased and T is lowered.
