Topological superfluids and the BEC-BCS crossover in the attractive Haldane-Hubbard model

Abstract

Motivated by the recent realization of the Haldane model in a shaking optical lattice, we investigate the effects of attractive interaction and the BEC-BCS crossover in this model at and away from half-filling. We show that, contrary to the usual s-wave BEC-BCS crossover in the lattice, a topological superfluid with Chern number C=2 appears in an extended region of the phase space for intermediate strength of the attractive interaction on the interaction-density plane. When inversion symmetry is broken, a gapless weak topological state is realized. We also investigate the fluctuations in these superfluid phases and show that the Anderson-Bogoliubov mode is quadratic due to time-reversal symmetry breaking and the existence of an undamped Leggett mode in the strong-coupling limit. Near the topological phase transition, the damping of the Leggett mode reaches its maximum.