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We describe the quantum phases of interacting three component fermions in thepresence of spin-orbit coupling, as well as linear and quadratic Zeeman fields.We classify the emerging superfluid phases in terms of the loci of zeros oftheir quasi-particle excitation spectrum in momentum space, and we identifyseveral Lifshitz-type topological transitions. In the particular case ofvanishing quadratic Zeeman field, a quintuple point exists where four gaplesssuperfluid phases with surface and line nodes converge into a fully gappedsuperfluid phase. Lastly, we also show that the simultaneous presence ofspin-orbit and Zeeman fields transforms a momentum-independent scalar orderparameter into an explicitly momentum-dependent tensor in the generalizedhelicity basis.

Quantum phases of interacting three-component fermions under the influence of spin-orbit coupling and Zeeman fields