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In some Dirac systems with time-reversal (T) and glide (G) symmetries,multihelicoid surface states (MHSSs) appear, as discussed in various systemssuch as electronic and photonic ones. However, the topological nature and theconditions for the appearance of the MHSSs have not been understood. Here weshow that MHSSs result from bulk-surface correspondence for the $Z_2$ monopolecharge Q, which cannot be defined as a local quantity associated with the Diracpoint, unlike the Z monopole charge characterizing Weyl points. The previouslyknown formula of Q turns out to be non-gauge-invariant and thus cannotcharacterize the MHSSs. This shortcoming of the definition of Q is amended byredefining Q as a global topological invariant in k-space. Surprisingly, thenewly defined Q, characterizing GT invariant gapless systems, is equal to theG-protected $Z_2$ topological invariant v, which is nontrivial only inT-breaking gapped systems. This global definition of Q automatically guaranteesthe appearance of MHSSs even when the Dirac point splits into Weyl points or anodal ring by lowering the symmetry, as long as the GT symmetry is preserved. Qcan be simplified to symmetry-based indicators when two vertical Gs arepreserved, and filling-enforced topological crystalline insulators arediagnosed in several cases when a T-breaking perturbation is induced. Materialcandidate Li2B4O7 together with a list of space groups preserving MHSSs arealso proposed.

$Z_2$ Dirac points with topologically protected multihelicoid surface states