  Weyl points, carrying a Z-type monopole charge C, have bulk-surface
correspondence (BSC) associated with helical surface states (HSSs). When |C| >
1, multi-HSSs can appear in a parallel manner. However, when a pair of Weyl
points carrying C = \pm 1 meet, a Dirac point carrying C = 0 can be obtained
and the BSC vanishes. Nonetheless, a recent study in Ref. [arXiv:2201.03238]
shows that a new BSC can survive for Dirac points when the system has
time-reversal (T )-glide (G) symmetry ({\Theta}=TG), i.e., anti-parallel
double/quad-HSSs associated with a new Z2-type monopole charge Q appears. In
this paper, we systematically review and discuss both the parallel and
anti-parallel multi-HSSs for Weyl and Dirac points, carrying two different
kinds of monopole charges. Two material examples are offered to understand the
whole configuration of multi-HSSs. One carries the Z-type monopole charge C,
shows both local and global topology for three kinds of Weyl points, and it
leads to parallel multi-HSSs. The other carries the Z2-type monopole charge Q,
only showing the global topology for {\Theta}-invariant Dirac points, and it is
accompanied by antiparallel multi-HSSs. These diverse topological surface
states not only offer the local and global topology for the bulk degeneracy but
also offer platforms to various topological phases.
