Topological Superfluids and BEC-BCS Crossover in Attractive Haldane-Hubbard Model

TL;DR

This paper explores topological superfluid phases and BEC-BCS crossover phenomena in the attractive Haldane-Hubbard model, revealing novel topological states and collective excitations influenced by interaction strength and symmetry breaking.

Contribution

It demonstrates the emergence of a topological superfluid with Chern number 2 and identifies a gapless topological state when inversion symmetry is broken, expanding understanding of superfluid phases in lattice models.

Findings

Topological superfluid with C=2 appears at intermediate attraction.

A gapless topological state emerges when inversion symmetry is broken.

Quadratic Anderson-Bogoliubov mode and undamped Leggett mode are identified.

Abstract

Motivated by the recent realization of the Haldane model in shaking optical lattice, we investigate the effects of attractive interaction and 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 phase space for intermediate strength of the attractive interaction in the interaction-density plane. When inversion symmetry is broken, a new gapless 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.