Exotic phase separation and phase diagrams of a Fermi-Fermi mixture in a trap at finite temperature

The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS-Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of ⁶Li and ⁴⁰K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the ⁶Li-⁴⁰K and other possible Fermi-Fermi mixtures.