A Unified Understanding of Diverse Spin Textures of Kramers–Weyl Fermions in Nonmagnetic Chiral Crystals

Abstract

AbstractChiral crystals, characterized by rotation, screw rotation, and translation symmetries are abundant in nature. The existence of Kramers–Weyl fermions (KWFs) at the time‐reversal‐invariant momenta in nonmagnetic chiral crystals (NCCs) has attracted intense attention due to their unique physical properties beyond conventional Weyl fermions. Although the spin texture, one of the most fundamental physical quantities, is found to be dramatically different for different KWFs in different NCCs, a unified understanding of this puzzling phenomenon is still lacking. In this article, combining k · p theory and first‐principles calculations, k‐linear Hamiltonians for KWFs are constructed and consequently a complete classification for the spin textures of KWFs in all the NCCs is made, which are confirmed by a series of material example calculations. Interestingly, it is found that the spin textures are reversed in NCCs with opposite chirality, leading to reversed Fermi arc surface states. Importantly, this study unveils that the nonlinear optical responses around the KWFs in NCCs can be largely determined by their spin texture classification. This study not only provides a unified understanding of the spin textures of KWFs in all the NCCs, but also suggests a principle to design novel KWF‐related spintronics and nonlinear optics.