High-order topological charge is of intensive interest in the field of topological matter. In real materials, a cubic Dirac point is rare, and the chiral charge of one Weyl point (WP) has never be found to exceed $\left|C\right|=3$ for spin-$\frac{1}{2}$ electronic systems. In this paper, we argue that a cubic Dirac point can result in one quadruple WP ($\left|C\right|=4$ with double band degeneracy) when time-reversal symmetry is broken, provided that this cubic Dirac point is away from the high-symmetry points and involves the coupling of eight bands, rather than the four bands that were thought to be sufficient to describe a Dirac point. The eight-band manifold can be realized in materials with screw symmetry. Near the zone boundary along the screw axis, the folded bands are coupled to their “parent” bands, resulting in doubling the dimension of the Hilbert space. Indeed, in $\varepsilon$-TaN (space group 194 with screw symmetry) we find a quadruple WP when applying a Zeeman field along the screw axis. This quadruple WP away from high-symmetry points is distinct from highly degenerate nodes at the high-symmetry points already reported. We further find that such a high chiral charge might be related to the parity mixing of bands with high degeneracy, which in turn alters the screw eigenvalues and the resulting chiral charge.

• Received 29 March 2020
• Revised 31 March 2021
• Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.115161