Symmetry-Protected Minimum of Four Conventional Weyl Points in Nonmagnetic Crystals

Abstract

Realizing nonmagnetic Weyl semimetals (WSMs) with the minimal number of conventional Weyl points (WPs) and a clean Fermi surface remains a central challenge. Here, combining symmetry analysis with first-principles calculations, we establish the definitive conditions under which a nonmagnetic crystal can host exactly four conventional ($C = \pm 1$) WPs, identifying 76 space groups in the spinless limit and 83 in the spinful case that allow this minimal configuration. Guided by this framework, we predict two previously unknown boron allotropes, P6-B$_{48}$ and TBIN-B$_{48}$, as ideal WSMs. Both exhibits precisely four isolated WPs near the Fermi level, with exceptionally clean electronic structures. Notably, the WPs in P6-B$_{48}$ are pinned to high-symmetry points, while those in TBIN-B$_{48}$ lie along high-symmetry lines, leading to distinct and experimentally accessible surface states, including single and double Fermi arcs. Our work provides a complete symmetry-based foundation and pristine material platforms for minimal Weyl physics.