Textures and exotic vortices in neutral fermion superfluids

There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in ³He-A phase and Feshbach-resonanced ⁶Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a half-quantum vortex in rotating superfluid ³He-A between parallel plates. (4) Majorana bound state in rotating superfluid ³He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid ³He community by stressing the importance of cross fertilization between them.