Two-dimensional imbalanced Fermi gas in antiparallel magnetic fields

We study a two-dimensional Fermi gas with an attractive interaction subjected to synthetic magnetic fields, which are assumed to be mutually antiparallel for two different spin components with population imbalance. By employing the mean-field approximation, we show that the Fulde-Ferrell state is energetically favored over the Larkin-Ovchinnikov state in the weak-coupling limit. We then elucidate the zero-temperature phase diagram in the space of attraction and two chemical potentials analytically at weak coupling as well as numerically beyond it. Rich structures consisting of quantum Hall insulator, unpolarized superfluid, and Fulde-Ferrell phases separated by various second-order and first-order quantum phase transitions are found.