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We discuss the evolution from BCS to Bose superfluidity for ultracoldfermions in two-dimensions and in the presence of simultaneous spin-orbit andZeeman fields. We analyze several thermodynamic properties to characterizedifferent superfluid phases including pressure, compressibility, inducedpolarization, and spin susceptibility. Furthermore, we compute the momentumdistribution and construct topological invariants for each of the superfluidphases.

Ultra-cold fermions in the flatland: evolution from BCS to Bose superfluidity in two-dimensions with spin-orbit and Zeeman fields