Classification of radial spin textures in chiral crystals

Radial spin textures in momentum space have been shown to appear around the Kramers-Weyl points of chiral crystals. Such spin textures are not unique to those band degeneracies, but they appear, regardless of the number of bands, at any high-symmetry point where at least two rotation or screw symmetry axes intersect. The two highest valence bands around the H point of trigonal Tellurium are an example of such radial spin texture in single degenerate bands [1]. In this work, we classify the different spin textures allowed by symmetry at the high-symmetry points of the chiral point groups. We found that basic spin textures in momentum space such as Hedgehog, Néel-type skyrmion and antiskyrmion can be found, but also much complex spin structures with cubic momentum dependence. We reveal all these spin textures in the band structure of Tellurium [2].
[1] M. Sakano et al. Phys. Rev. Lett. 124, 136404 (2020).
[2] G. Gatti et al. Phys. Rev. Lett. (in press)