Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

手性晶体是具有晶格结构的材料，由于缺乏反型，镜面或其他旋转反转对称性，其具有明确的手性。尽管已经证明晶体对称性的存在可以保护拓扑带越界，但是手性晶体的拓扑电子性质在很大程度上仍未表征。在这里，我们证明Kramers-Weyl费米子是具有自旋-轨道耦合的所有非磁性手性晶体的通用拓扑电子性质，并通过结构手性，晶格平移和时间反转对称性得到保证。与传统的韦尔费米子不同，它们出现在时间反转不变的时刻。我们在65个手性空间组中的33个中确定了代表性的手性材料，其中Kramers-Weyl费米子与低能物理学有关。我们确定，具有相关自旋-轨道耦合的非磁性手性晶体中的所有点状节点简并都带有非平凡的Chern数。克雷默斯-魏尔材料在异常大的能量窗口上会表现出单极子状的电子自旋结构和拓扑上不平凡的大量费米表面。