Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In stark contrast, here we report that Weyl points in systems that are symmetric under the composition of time reversal with a π rotation are characterized by a non-Abelian topological invariant. The topological charges of the Weyl points are transformed via braid phase factors, which arise upon exchange inside symmetric planes of the reciprocal momentum space. We elucidate this process with an elementary two-dimensional tight-binding model that is implementable in cold-atom set-ups and in photonic systems. In three dimensions, interplay of the non-Abelian topology with point-group symmetry is shown to enable topological phase transitions in which pairs of Weyl points may scatter or convert into nodal-line rings. By combining our theoretical arguments with first-principles calculations, we predict that Weyl points occurring near the Fermi level of zirconium telluride carry non-trivial values of the non-Abelian charge, and that uniaxial compression strain drives a non-trivial conversion of the Weyl points into nodal lines.

三维晶体中的Weyl半金属提供了受拓扑保护的能带节点的范例。通常认为，每对碰撞的Weyl点带有相反的手性电荷时，它们都会被歼灭。与之形成鲜明对比的是，在这里我们报告，在具有π旋转的时间反转的组成下对称的系统中的Weyl点具有非阿贝尔拓扑不变性的特征。Weyl点的拓扑电荷是通过编织相位因子转换的，编织相位因子是在相互动量空间的对称平面内交换时产生的。我们使用基本的二维紧密绑定模型阐明了此过程，该模型可在冷原子设置和光子系统中实施。在三个方面，非阿贝尔拓扑结构与点组对称性的相互作用显示出实现拓扑相变的作用，其中成对的Weyl点可能散射或转换为节点线环。通过将我们的理论论证与第一性原理计算相结合，我们可以预测在碲化锆费米能级附近出现的Weyl点带有非阿贝尔电荷的非平凡值，并且单轴压缩应变会驱动Weyl的非平凡转换。指向节点线。