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

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.

25 pages, 12 figures

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Cited by in corpus (5)

• Topological transition from nodal to nodeless Zeeman splitting in altermagnets
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials
• Irreducible momentum-space spin structure of Weyl semimetals and its signatures in Friedel oscillations
• Standard model of electromagnetism and chirality in crystals