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Predominant electronic order parameter for structural chirality: Role of spinless electronic toroidal multipoles in Te and Se

Rikuto Oiwa1,2,* and Hiroaki Kusunose3

  • *Contact author: roiwa@sci.hokudai.ac.jp
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Phys. Rev. Research 7, 033250 – Published 15 September, 2025

DOI: https://doi.org/10.1103/1zq8-pqh8

Abstract

We discuss predominant order parameters for structural chirality and demonstrate that time-reversal-even axial quadrupole plays a key role in stabilizing a chiral structure. Using the symmetry-adapted closest Wannier model of the trigonal Te and Se, we quantify the evolution of the spin-independent (spinless) and spin-dependent (spinful) electric toroidal (ET) (axial) multipole moments across the transition from an achiral to a chiral structure. Our results clearly identify that a spin-independent off-diagonal real hopping between p orbitals, which corresponds to the bond-cluster spinless ET quadrupole of (3z2−r2) type Gu, is the predominant order parameter in stabilizing helical structures. We further elucidate that the above itinerant spinless ET quadrupole induces a monopolelike orbital angular momentum texture in the momentum space, which can be observed via circular dichroism in soft x-ray photoemission spectroscopy measurement. Our findings highlight a critical role of the orbital angular momentum in chiral materials rather than less dominant spin angular momentum arising from the relativistic spin-orbit coupling.

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Phys. Rev. Research 7, 033250– Published 15 September, 2025
  • Received 13 April 2025
  • Accepted 22 August 2025
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