Monopole Superconductivity with Half-integer Partial-wave Symmetries

The pairing symmetries of superconducting gap functions are usually of integer partial-waves (s,p,d, and etc). In this work, we study a new class of topological superconducting states whose gap functions possess half-integer partial-wave symmetries. These exotic states can exist in systems with topological Fermi surfaces possessing non-zero Chern numbers. When pairing occurs between Fermi surfaces whose Chern numbers are differed by an odd integer, the corresponding superconducting gap function is represented by monopole harmonics with half-integer monopole charges, and thus carries spinor partial-wave symmetries. Topological properties of this class of states, including the surface Majorana modes are studied. We also discuss the possible experimental realizations in Weyl semi-metal system and ultra-cold atom systems.