  We generalize the concept of Berry connection of the single-electron band
structure to the two-particle Cooper pair states between two Fermi surfaces
with opposite Chern numbers. Because of underlying Fermi surface topology, the
pairing Berry phase acquires non-trivial monopole structure. Consequently,
pairing gap functions have the topologically-protected nodal structure as
vortices in the momentum space with the total vorticity solely determined by
the monopole charge $q_p$. The pairing nodes behave as the Weyl-Majorana points
of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the
connection patterns of the surface modes from the Weyl band structure and the
Majorana surface modes inside the pairing gap is also discussed. Under the
approximation of spherical Fermi surfaces, the pairing symmetry are represented
by monopole harmonic functions. The lowest possible pairing channel carries
angular momentum number $j=|q_p|$, and the corresponding gap functions are
holomorphic or anti-holomorphic functions on Fermi surfaces.
