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We analyze the interplay of adiabatic rotation and Rashba spin-orbit couplingon the BCS-BEC evolution of a harmonically-trapped Fermi gas in two dimensionsunder the assumption that vortices are not excited. First, by taking thetrapping potential into account via both the semi-classical and exactquantum-mechanical approaches, we firmly establish the parameter regime wherethe non-interacting gas forms a ring-shaped annulus. Then, by taking theinteractions into account via the BCS mean-field approximation, we study thepair-breaking mechanism that is induced by rotation, i.e., the Corioliseffects. In particular, we show that the interplay allows for the possibilityof creating either an isolated annulus of rigidly-rotating normal particlesthat is disconnected from the central core of non-rotating superfluid pairs oran intermediate mediator phase where the superfluid pairs and normal particlescoexist as a partially-rotating gapless superfluid.

Rotating a Rashba-coupled Fermi gas in two dimensions