Extended $s$-wave superfluid of repulsively interacting three-component fermionic atoms in optical lattices

We investigate pairing symmetry of the superfluid state in repulsively interacting three-component (colors) fermionic atoms in optical lattices. This superfluid state appears, when two of the color-dependent three repulsions are much stronger than the other close to half filling [1]. We evaluate the effective pairing interaction by collecting random-phase-approximation-type diagrams and ladder diagrams, and solve the Eliashberg equation within weak-coupling theory in square optical lattices. We find that pairing symmetry is an extended $s$-wave, although in the phase diagram the superfluid state is adjacent to the color-density wave or paired Mott insulator at half filling. The $k$-dependence of the superfluid order parameter is caused by quantum fluctuations of the staggered color-density wave. When the difference in the three repulsions is decreased, paring symmetry changes from an extended $s$-wave to a $d$-wave. We expect $^{6}$Li, $^{171}$Yb, $^{173}$Yb atoms and their mixtures in optical lattices to be possible candidates for observing this superfluid state.\\[0pt] [1] K. Inaba and S. Suga, \textit{Phys. Rev. Lett.} \textbf{108} (2012) 255301.