Spinless Fulde-Ferrell superfluid in Haldane model with nearest-neighbor interaction.

Fulde-Ferrell (FF) state is an exotic superconducting or superfluid state, characterized by Cooper pairs with a finite center-of-mass momentum, and it has been intensively investigated in spinful systems, but the spin population imbalance is usually necessary. Here we propose a model to realize and modulate the spinless FF superfluid, namely, Haldane model with nearest-neighbor interaction. The FF state appears when the space-inversion and time-reversal symmetries are broken simultaneously, and there exists the first order phase transition. A higher Berezinskii-Kosterlitz-Thouless transition temperature is obtained at larger absolute value of Peierls phase and smaller energy offset of the sublattices. Our proposal provides a feasible option for experimental researchers to detect the FF superfluid.