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

Abstract

Chiral 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.

Parallel spin-momentum locking in a chiral topological semimetal

“…In the context of multifold fermions, Refs. [24,25] apply to Fermi pockets far enough from the nodal point such that bands are only weakly spin-split; this complements the approach of Ref. [4] which is applicable much closer to the nodal point, where bands cannot be described in a simple spin-orbit decoupled basis.…”

“…Additionally, Refs. [24,25] considered the spin texture in chiral crystals for bands that can be treated in the limit of weak SOC, and derived the possible spin textures for weakly spin-split Fermi surfaces, finding many cases where chiral cubic symmetry enforces perfectly parallel SML along generic momentum directions. In the context of multifold fermions, Refs.…”

“…S5 for a band structure calculation without SOC), parallel SML is also consistent with the prediction of Refs. [24,25] for B20 crystal structure.…”

Fermiology of Chiral Cadmium Diarsenide CdAs2, a Candidate for Hosting Kramers–Weyl Fermions

“…10−12 Even in their nonmagnetic state, these chiral crystals show universal topological electronic properties due to their spin−orbit coupling and crystalline chirality, resulting in the presence of Kramers−Weyl Fermions in their spectrum. 13,14 These Fermions are pinned to Kramers degenerate points, leading to the appearance of topological gaps, which are significantly larger than those observed in Weyl semimetals. 13 Within such gaps, ubiquitous topological properties, such as quantized chiral charges, 15 negative longitudinal magnetoresistance, 16 and nontrivial Chern numbers 17 can arise, opening up exciting avenues for engineering exotic transport phenomena and applications.…”

“…13,14 These Fermions are pinned to Kramers degenerate points, leading to the appearance of topological gaps, which are significantly larger than those observed in Weyl semimetals. 13 Within such gaps, ubiquitous topological properties, such as quantized chiral charges, 15 negative longitudinal magnetoresistance, 16 and nontrivial Chern numbers 17 can arise, opening up exciting avenues for engineering exotic transport phenomena and applications. Furthermore, Kramers−Weyl Fermions differ from conventional Weyl Fermions as they occur at timereversal invariant points in momentum space.…”