Abstract
By analyzing vortex lattices, re-entrant Cooper pairing and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a single theoretical framework we explore how vortices and spin textures join to protect superconductivity against large magnetic fields. We use a rapidly rotating ultra-cold gas of fermionic atoms near unitarity as a model system amenable to experimental exploration, and discover a hierarchy of spin-polarized and FFLO phases in which a metal or a band-insulator of unpaired particles coexists with a spatially modulated superfluid hosting a vortex lattice. Quantum fluctuations can transform these phases into strongly correlated "vortex liquid" metals and insulators respectively. We argue that vortex lattices significantly enhance the stability of FFLO states and discuss prospects for observing these states in cold atom experiments.
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