Based on ab initio relativistic k⋅p theory, we derive an effective two-band model for surface states of three-dimensional topological insulators up to seventh order in k. It provides a comprehensive description of the surface spin structure characterized by a non-orthogonality between momentum and spin. We show that the oscillation of the non-orthogonality with the polar angle of k with a π/3 periodicity can be seen as due to effective six-fold symmetric spin-orbit magnetic fields with a quintuple and septuple winding of the field vectors per single rotation of k. Owing to the dominant effect of the classical Rashba field, there remains a single-winding helical spin structure but with a periodic few-degree deviation from the orthogonal locking between momentum and spin.
@article{arxiv.2005.14557,
title = {Ab initio k.p theory of spin-momentum locking: Application to topological surface states},
author = {I. A. Nechaev and E. E. Krasovskii},
journal= {arXiv preprint arXiv:2005.14557},
year = {2020}
}