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We show that spin-orbit coupling (SOC) gives rise to pairing instability in ahighly polarized two-dimensional Fermi gas for arbitrary interaction strength.The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-likemolecular state, which undergoes a first-order transition into a pairing statewith zero center-of-mass momentum as the parameters are tuned. These pairingstates are metastable against a polaron state dressed by particle-holefluctuations for small SOC. At large SOC, a polaron-molecule transition exists,which suggests a phase transition between the topological superfluid state andthe normal state for a highly polarized Fermi gas in the thermodynamic limit.As polarization in a Fermi gas with SOC is induced by the effective Zeemanfield, we also discuss the influences of the effective Zeeman field on theground state of the system. Our findings may be tested directly in futureexperiments.

Molecule and polaron in a highly polarized two-dimensional Fermi gas with spin-orbit coupling