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

TL;DR

This paper develops an advanced ab initio k·p model for topological insulator surface states, revealing complex spin-momentum locking behaviors influenced by higher-order effects and spin-orbit fields.

Contribution

It introduces a detailed two-band effective model up to seventh order in k, capturing non-orthogonal spin-momentum locking and complex spin textures in topological surface states.

Findings

Oscillation of non-orthogonality with π/3 periodicity

Effective six-fold symmetric spin-orbit magnetic fields

Single-winding helical spin structure with deviations

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.