Phase- and temperature-driven chiral topological superfluids on a honeycomb lattice

The correlated spinful Haldane model exhibits rich topological phases consisting of chiral topological superfluids (TSFs) and topological spin density waves. However, most of previous studies mainly focus on the case with the fixed hopping phase or at zero temperature. In this paper, we study the attractive spinful Haldane model with arbitrary phase at finite temperature. The chiral TSFs with Chern numberC = 2 and 4 emerge driven by the phase and temperature. In particular, the temperature can drive aC = 2 topological superfluid from a trivial normal insulator phase at an appropriate interaction. The bulk topology of all TSFs is uncovered by the Wilson loop method, and confirmed by the responses of edge dislocations.