  We study the possibility of angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
state, in which the rotation symmetry is spontaneously broken, in population
imbalanced fermion gases near the BCS-BEC crossover. We investigate the
superfluid gases at low temperatures on the basis of the Bogoliubov-de Gennes
equation, and examine the stability against thermal fluctuations using the
T-matrix approach beyond the local-density approximation (LDA). We find that
the angular FFLO state is stabilized in the gases confined in the toroidal trap
but not in the harmonic trap. The angular FFLO state is stable near the BCS-BEC
crossover owing to the formation of pseudogap. Spatial dependences of number
density and local population imbalance are shown for an experimental test.
