Exotic paired fermion state mapped onto a spherical shell

Solving the Bogoliubov-de Gennes equations on a thin spherical shell, the authors map out where ordinary uniform superfluidity breaks down in a spin-polarized Fermi gas and where the exotic Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state — characterized by a spatially oscillating order parameter — can take over. LOFF states with more nodes in the order parameter become energetically preferred at higher spin polarization, but they survive only in a narrow sliver near the boundary where uniform superfluidity disappears. The result quantifies the geometric fragility of LOFF pairing on curved compact surfaces, relevant to ultracold gas experiments using shell-trap geometries.