  We demonstrate that a class of stable $\mathbb{Z}_2$ monopole charge Dirac
point ($\mathbb{Z}_2$DP) phases can robustly exist in real materials, which
surmounts the understanding: that is, a $\mathbb{Z}_2$DP is unstable and
generally considered to be only the critical point of a $\mathbb{Z}_2$ nodal
line ($\mathbb{Z}_2$NL) characterized by a $\mathbb{Z}_2$ monopole charge (the
second Stiefel-Whitney number $w_2$) with space-time inversion symmetry but no
spin-orbital coupling. For the first time, we explicitly reveal the
higher-order bulk-boundary correspondence in the stable $\mathbb{Z}_2$DP phase.
We propose the alternating-twisted multilayer graphene, which can be regarded
as 3D twisted bilayer graphene (TBG), as the first example to realize such
stable $\mathbb{Z}_2$DP phase and show that the Dirac points in the 3D TBG are
essential degenerate at high symmetric points protected by crystal symmetries
and carry a nontrivial $\mathbb{Z}_2$ monopole charge ($w_2=1$), which results
in higher-order hinge states along the entire Brillouin zone of the $k_z$
direction. By breaking some crystal symmetries or tailoring interlayer coupling
we are able to access $\mathbb{Z}_2$NL phases or other $\mathbb{Z}_2$DP phases
with hinge states of adjustable length. In addition, we present other 3D
materials which host $\mathbb{Z}_2$DPs in the electronic band structures and
phonon spectra. We construct a minimal eight-band tight-binding lattice model
that captures these nontrivial topological characters and furthermore tabulate
all possible space groups to allow the existence of the stable $\mathbb{Z}_2$DP
phases, which will provide direct and strong guidance for the realization of
the $\mathbb{Z}_2$ monopole semimetal phases in electronic materials,
metamaterials and electrical circuits, etc.
