Cubic Dirac and quadruple Weyl points in screw-symmetric materials

TL;DR

This paper predicts and demonstrates the existence of quadruple Weyl points with chiral charge |C|=4 in screw-symmetric materials, expanding understanding of high-order topological charges in topological matter.

Contribution

It introduces the concept that cubic Dirac points can lead to quadruple Weyl points in materials with screw symmetry, involving eight-band coupling and breaking time-reversal symmetry.

Findings

Quadruple Weyl points found in ε-TaN under Zeeman field

High chiral charge linked to parity mixing of high-degeneracy bands

Distinct from previously known high-symmetry point degeneracies

Abstract

High-order topological charge is of intensive interest in the field of topological matters. In real materials, cubic Dirac point is rare and the chiral charge of one Weyl point (WP) has never be found to exceed |C| = 3 for spin- 1/2 electronic systems. In this work, we argue that a cubic Dirac point can result in one quadruple WP (|C| = 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 coupling of eight bands, rather than 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 dimension of the Hilbert space. Indeed, in "$\epsilon$-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 resulted chiral charge.