Ab initio k.p theory of spin-momentum locking: Application to topological surface states

Abstract

Based on ab initio relativistic $\mathbf{k}\cdot \mathbf{p}$ theory, we derive an effective two-band model for surface states of three-dimensional topological insulators up to seventh order in $\mathbf{k}$. 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 $\mathbf{k}$ with a $\pi /3$ 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 $\mathbf{k}$. 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.

arXiv comment8 pages, 3 figures, 2 tables

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Cited by in corpus (3)

• Non-orthogonal Spin-Momentum Locking
• Variety of scenarios of the magnetic exchange response in topological insulators
• Spatial aspects of spin polarization of structurally split surface states in thin films with magnetic exchange and spin-orbit interaction