Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

TL;DR

This paper classifies topologically protected band touchings like Weyl points and nodal lines in magnetic materials based on their symmetry groups, providing a comprehensive framework for identifying topological semimetals.

Contribution

It introduces a symmetry-based classification scheme for twofold-degenerate band touchings in spin-1/2 systems across all magnetic point groups, applicable throughout the Brillouin zone.

Findings

All magnetic point groups without inversion-time-reversal product can host topological nodes.

Classification applies to every momentum point via little group analysis.

Nodes are common and do not require complex multiband interactions.

Abstract

Symmetry-protected topological semimetals are at the focus of solid-state research due to their unconventional properties, for example, regarding transport. By investigating local two-band Bloch Hamiltonians in the spin-1/2 basis for the 122 magnetic point groups, we classify twofold-degenerate band touchings such as Weyl points, robust nodal lines on axes and in mirror planes, and fragile nodal lines. We find that all magnetic point groups that lack the product of inversion and time-reversal symmetries can give rise to topologically nontrivial band touchings. Hence, such nodes are the rule rather than the exception and, moreover, do not require any complicated multiband physics. Our classification is applicable to every momentum in the Brillouin zone by considering the corresponding little group and provides a powerful tool to identify magnetic and nonmagnetic topological semimetals.