  Topological fermions as excitations from multi-degenerate Fermi points have
been attracting increasing interests in condensed matter physics. They are
characterized by topological charges, and magnetic fields are usually applied
in experiments for their detection. Here we present an index theorem that
reveals the intrinsic connection between the topological charge of a Fermi
point and the in-gap modes in the Landau band structure. The proof is based on
mapping fermions under magnetic fields to a topological insulator whose
topological number is exactly the topological charge of the Fermi point. Our
work lays a solid foundation for the study of intriguing magneto-response
effects of topological fermions.
