Fulde−Ferrell−Larkin−Ovchinnikov states in two-dimensional non-Hermitian fermionic superfluidity

We investigate a two-dimensional non-Hermitian Fermi system with spin imbalance and dissipative interaction. We employ the mean-field approximation to derive and minimize the thermodynamic potential, and determine the zero-temperature phase diagram upon variation of imbalance and dissipation. Notably, we identify a Fulde−Ferrell−Larkin−Ovchinnikov (FFLO) state characterized by a pairing order parameter with finite center-of-mass momentum, along with the normal, Bardeen−Cooper−Schrieffer (BCS), and metastable BCS states. The FFLO state is favored with increasing spin imbalance but diminishes and eventually disappears with elevated dissipation. Additionally, we present the quasiparticle energy spectrum and momentum distribution, highlighting the spatial asymmetry features that can be used to deterministically identify the FFLO state.