Exotic superfluid with emergent flux in a one-dimensional Bose-Fermi mixture

We find a chiral superfluid (CSF) phase in a one-dimensional Bose-Fermi Hubbard model with significant mass and density imbalance between the two species. In the CSF phase, bosons condensate at nonzero momentum $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/L$ with chain length $L$. To capture the essential physics of this phenomenon, we study an alternative simplified model that only features competition between single-fermion hopping and hopping of composite particles composed of a fermion and a boson. This model captures the low-energy physics of the Hubbard model and hosts a robust CSF phase. Our numerical studies show that in the CSF phase, the local superfluid order parameter continuously rotates along the chain, indicating that time-reversal symmetry is spontaneously broken. This symmetry breaking generates an emergent flux in the background, effectively optimizing the system's ground-state energy. We provide a physical understanding at the mean-field level. Furthermore, we have explored the potential realization of this phase in cold-atom experiments.