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In chiral crystals, the absence of inversion and mirror symmetry is responsible for unconventional spin properties and the emergence of exotic topological fermions [1]. Trigonal tellurium is one of the simplest chiral crystals, and by using spin-and-angle-resolved photoemission spectroscopy (srARPES) we have recently reported signatures of composite, accordionlike and Kramers-Weyl (KW) fermions in its band structure [2]. In contrast to conventional Weyl fermions that arise from band inversion, and are thereby degenerate in energy, KW points with opposite topological charges are pinned at different energies and at different time-reversal invariant momenta (TRIM) by the action of time-reversal symmetry.
In KW fermions the spin is predicted to lie parallel to the wavevector, thus realizing a hedgehog texture [1]. In our study we clarify that the radial spin texture is not a prerogative of the KW fermions, but it can be observed also at non-TRIM point [2], as confirmed by an independent srARPES study of the spin properties around the H point of Te [3]. This is made possible by the presence of multiple rotational axes, combined with the breaking of mirror symmetry. Our results illustrate how the arrangement of spin in the reciprocal space is a consequence of the local point group symmetry, and it does not reflect only global properties of the crystal. Spin texture more complex than hedgehog-like can be stabilized, sharing common features with the arrangement taken in Skyrmions by magnetic momenta in real space [3, 4]. These spin textures are important ingredient to explain the chiral induced spin selectivity (CISS) effect that might find application in spintronics devices [5]; hence a complete classification of the spin texture for all local point group symmetries is highly demanded.
[1] G. Chang et al., Nat. Mater. 17, 978 (2018)
[2] G. Gatti et al., Phys. Rev. Lett. 125, 216402 (2020)
[3] M. Sakano et al., Phys. Rev. Lett. 124, 136404 (2020)
[4] C.M. Acosta et al., Phys. Rev. B 104, 104408 (2021)
[5] S. Dalum and P. Hedegård, Nano Lett. 19, 5253 (2019)
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