Three-dimensional spin–orbit coupled Fermi gases: Fulde–Ferrell pairing, Majorana fermions, Weyl fermions, and gapless topological superfluidity*
Liu Xia-Jia), Hu Huia), Pu Hanb),c)†
       
(a) Evolution of the superfluid phase with increasing in-plane Zeeman field at zero out-of-plane Zeeman field h out = 0. Driven by the in-plane field only, the system evolves from a gapped FF superfluid to a gapless FF state, and then to a topologically non-trivial FF superfluid with either four (gapless topo-FF4) or two Weyl nodes/loops (gapless topo-FF2). The solid and dashed lines show the energy at k = 0 [ E 2+( k = 0)] and the minimum energy [min E 2+( k )] of the lower particle branch. The inset shows the chemical potential, pairing gap and FF pairing momentum as a function of the in-plane Zeeman field. (b) The energy of the lower particle branch along the k y direction, E 2+( k x = 0, ky , kz = 0), at h in/ E F = 0.30 (gapless FF, dashed line), 0.33 (gapless topo-FF4, thin solid line), and 0.40 (gapless topo-FF2, thick solid line). The minimum energy touches zero at the positions of Weyl nodes.