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  • Open Access

Universal classification of Weyl semimetals via sixteen irreducible Weyl molecules

Ke-Xin Pang*, Hui-Jing Zheng*, and Yan Gao†

  • State Key Laboratory of Metastable Materials Science and Technology and Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao 066004, China

  • *These authors contributed equally to this work.
  • †Contact author: yangao9419@ysu.edu.cn
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Phys. Rev. Research 8, 033304 – Published 14 September, 2026

DOI: https://doi.org/10.1103/qwrz-9xm9

Abstract

Governed by the Nielsen-Ninomiya theorem, Weyl points (WPs) function as topological monopoles that cannot exist in isolation but must form charge-neutral assemblies in the momentum space of crystals. While these WPs are locally characterized by quantized chiral charges, the finite generating family governing their global assembly into a Weyl semimetal (WSM) phase remains undiscovered. Here, we resolve this by identifying “irreducible Weyl molecules” (IWMs) as the elementary, charge-neutral topological building blocks of WSMs. By rigorously imposing the constraints of 1651 magnetic space groups on minimal zero-sum chiral-charge sequences, we obtain exactly 16 crystallographically realizable IWMs. We establish a universal linear-combination principle, demonstrating that any crystallographically realizable charge-neutral chiral-node configuration Y within |C|≤4 is constructed from a linear superposition of these 16 generators Xi with non-negative integer coefficients ni, governed by Y=∑i=116niXi. Utilizing first-principles calculations on a predicted family of boron allotropes, we reveal that this superposition principle organizes the bulk nodal configurations and constrains the admissible end point connectivity of Fermi arcs, while the realized surface geometry remains dependent on termination, energy, and allowed inter-IWM reconstruction. Our work establishes a “periodic table” for WSMs, offering a general theoretical framework for the classification and rational design of Weyl complexes.

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Phys. Rev. Research 8, 033304– Published 14 September, 2026
  • Received 3 December 2025
  • Revised 25 April 2026
  • Accepted 13 August 2026
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