Stable higher-order topological Dirac semimetals with Z2 monopole charge in alternating-twist multilayer graphene and beyond

We demonstrate that a class of stable Z2 monopole charge Dirac point (Z2DP) phases can robustly exist in real materials, which is counterintuitive: that is, a Z2DP is unstable and generally considered to be only the critical point of a Z2 nodal line (Z2NL) characterized by a Z2 monopole charge (the second Stiefel-Whitney number w2) with space-time inversion symmetry but no spin-orbital coupling. We explicitly reveal the higher-order bulk-boundary correspondence in the stable Z2DP phase. We propose the alternating-twist multilayer graphene, which can be regarded as 3D twisted bilayer graphene (TBG), as the first example to realize such stable Z2DP phase and show that the Dirac points in the 3D TBG are essentially degenerate at high-symmetry points protected by crystal symmetries and carry a nontrivial Z2 monopole charge (w2=1), which results in higher-order hinge states along the entire Brillouin zone of the kz direction. By breaking some crystal symmetries or tailoring interlayer coupling we are able to access Z2NL phases or other Z2DP phases with hinge states of adjustable length. In addition, we present other 3D materials which host Z2DPs 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 Z2DP phases, which will provide direct and strong guidance for the realization of the Z2 monopole semimetal phases in (among others) electronic materials, metamaterials, and electrical circuits.