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We show the spin-orbital coupling induced by an artificial light-inducedgauge field can fully restore superfluidity suppressed by population imbalancein a two-dimensional (2D) Fermi gas, leading to unconventional superfluidstates either with topological Majorana fermion excitations or showing a novelmixture of triplet pairing with spin-up (down) components respectively in the$p_{x}\pm ip_{y}$ pairing channels. We self-consistently calculate the zerotemperature phase diagram at the BCS\ side of Feshbach resonance and show thatthe phase transitions between different superfluid states can be revealedthrough measurement of the in-situ density profile of the 2D atomic cloud in aweak global trap.

Unconventional superfluidity induced by spin-orbital coupling in a polarized two-dimensional Fermi gas