Realization of charge-four Weyl point in fermionic systems

Unconventional quasiparticles of a twofold band degeneracy with $|C|=4$, named as charge-four Weyl point (CFWP), have been revealed in bosonic and artificial systems, while it is challenging in fermionic systems because of nonnegligible spin-orbit coupling. Herein, we propose a carbon allotrope, termed cP-C24, as an ideal platform to realize CFWP in the nonrelativistic limit. Besides one CFWP ($C=+4$), there are also eight type-I Weyl points ($C=+1$) and twelve type-II Weyl nodes ($C=\ensuremath{-}1$), making the topological charge in the whole Brillouin zone to be neutral. The characteristic quadruple helicoid surface states of CFWP are presented. Our work offering the avenue of CFWP in fermionic systems would absolutely advance the research on the chirality-dependent physical properties associated with unconventional topological quasiparticles.