Chiral ferromagnetism in a trapped Fermi gas with a large spin-orbit coupling

A large spin-orbit (SO) coupling gives rise to a list of Landau level-like flat bands in a harmonic trap. In this work, we show that a chiral ferromagnetism in a trapped Fermi gas would appear on this flat bands for a weakly repulsive interaction. The competition between the ferromagnetic state with the strongly correlated state is studied. Due to the SO coupling, the spin ordering drives a corresponding orbital ordering, i.e., a chiral density current in the ferromagnetic phase. The experimental study of the these results obtained in this paper is discussed.