Cubic Dirac and quadruple Weyl points in screw-symmetric materials

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