Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice

The pairing symmetry of interacting Dirac fermions on the $\pi$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked cluster expansion methods. The extended $s^{\ast }$- (i.e. extended $s$-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an exotic $d{s}^{\ast }$-wave phase consisting of alternating stripes of $s^{\ast }$- and d-wave phases. A complementary mean-field analysis shows that while the $s^{\ast }$- and d-wave symmetries individually have nodes in the energy spectrum, the $d{s}^{\ast }$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.