Single-pair charge-2 Weyl-Dirac composite semimetals

TL;DR

This paper classifies magnetic space groups to identify conditions for a minimal charge-2 Weyl-Dirac composite semimetal state, predicts its realization in chiral boron allotropes, and confirms its electronic structure and surface states through first-principles calculations.

Contribution

It provides the first complete classification of MSGs supporting charge-2 Weyl-Dirac states and predicts a real material realization in chiral boron structures.

Findings

Only specific MSGs support the charge-2 Weyl-Dirac state.

First-principles calculations confirm the existence of charge-2 Weyl and Dirac points.

The predicted material exhibits ultralong Fermi arcs linked to structural chirality.

Abstract

The Nielsen--Ninomiya theorem requires that the total topological chiral charges in a crystal vanish, a constraint typically satisfied by identical nodes like Weyl--Weyl pairs. Whether a minimal heterogeneous configuration -- comprising a single Weyl point (WP) and a single Dirac point (DP) -- can exist in an electronic system has remained unresolved. Here, by systematically classifying all 1651 magnetic space groups (MSGs), we reveal that only 14 MSGs without spin-orbit coupling (SOC) and 10 MSGs with SOC are compatible with this exotic state. Furthermore, for nonmagnetic crystals, this configuration is uniquely realized in the spinless limit of chiral space groups 92 and 96. Guided by this principle, we predict an ideal realization in chiral three-dimensional boron allotropes (SDHBN-B$_{28}$ enantiomers). First-principles calculations unveil a $|C|=2$ WP at the $\Gamma$ point and a $|C|=2$ DP at the $A$ point, which constitute the only fermions near the Fermi level within a large $2$ eV energy window. Strikingly, the structural chirality rigidly dictates the sign of the topological charges, yielding two ultralong Fermi arcs spanning the surface Brillouin zone. Our work provides a complete crystallographic classification and a definitive material platform for exploring minimal heterogeneous chiral fermions.