  In addition to the conventional contribution that is directly controlled by
the single-particle energy spectrum, the superfluid phase stiffness of a
two-component Fermi gas has a geometric contribution that is governed by the
quantum metric of the honeycomb's band structure. Here, we take both
contributions into account, and construct phase diagrams for the critical
superfluid transition temperature as a function of the chemical potential,
particle filling, onsite interaction and next-nearest-neighbor hopping. Our
theoretical approach is based on a self-consistent solution of the BCS
mean-field theory for the stationary Cooper pairs and the universal BKT
relation for the phase fluctuations.
