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We report the equilibrium vortex phase diagram of a rotating two-band Fermigas confined to a cylindrically symmetric parabolic trapping potential, usingthe recently developed finite-temperature effective field theory [Phys. Rev. A$\bf{94}$, 023620 (2016)]. A non-monotonic resonant dependence of the freeenergy as a function of the temperature and the rotation frequency is revealedfor a two-band superfluid. We particularly focus on novel features that appearas a result of interband interactions and can be experimentally resolved. Theresonant dependence of the free energy is directly manifested in vortex phasediagrams, where areas of stability for both integer and fractional vortexstates are found. The study embraces the BCS-BEC crossover regime and theentire temperature range below the critical temperature $T_{c}$. Significantlydifferent behavior of vortex matter as a function of the interband coupling isrevealed in the BCS and BEC regimes.

Diversified vortex phase diagram for a rotating trapped two-band Fermi gas in the BCS-BEC crossover