Non-Abelian Berry phase and Chern numbers in higher spin-pairing condensates

We show that the non-Abelian Berry phase emerges naturally in the s-wave and spin quintet pairing channel of spin- 3/2 fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This topological structure can be realized in ultracold atomic systems and in solid state systems with at least two Kramers doublets.