Doubly charged single Weyl pair with complete spin polarization†

Topological states in crystalline materials have aroused significant research attention in recent years and have been expanded into intrinsic magnetic materials and high-order conditions. These investigations offer intriguing prospects from a fundamental physics standpoint. However, the combination of these aspects presents a great challenge as ideal material candidates with both clean band structures and simple topological configurations are extremely limited. Consequently, there have been only scarce investigations in this perspective. In this study, an ideal charge-two single Weyl pair with complete spin polarization has been unveiled in the Cu-doped lead apatite Pb₉Cu(PO₄)₆O. The topological surface states under the ±2 chiral topological charge can be prominently observed, making them immediately ready for experimental inspection since this material has already been synthesized. Detailed symmetry arguments and Hamiltonian analysis have been provided and, moreover, this simple topological configuration exhibits strong robustness against large strain conditions. These discoveries lay the groundwork for exploring the topological properties with both magnetic ordering and high-order dispersion. Importantly, the presented material candidates can instantly inspire the corresponding experimental advances and even revolutionize the field of spintronic topology.