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

TL;DR

This paper identifies symmetry conditions for nonmagnetic crystals to host exactly four Weyl points, predicts two new boron allotropes as ideal Weyl semimetals, and discusses their unique electronic and surface state features.

Contribution

It provides a comprehensive symmetry-based framework for realizing minimal Weyl points and predicts two new boron structures as candidate materials.

Findings

76 space groups allow four Weyl points in spinless limit

83 space groups allow four Weyl points in spinful case

Two boron allotropes predicted with exactly four Weyl points and distinct surface states

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.