Spin texture of generic helical edge states

TL;DR

This paper investigates the spin texture of helical edge states in topological insulators, revealing a universal momentum-dependent rotation of the spin quantization axis across various lattice models and geometries, and proposes a spectroscopy method to observe this phenomenon.

Contribution

It demonstrates the universal presence of a momentum-dependent spin rotation in helical edge states regardless of lattice type or geometry, extending understanding of spin textures in topological insulators.

Findings

Universal momentum-dependent spin rotation in helical edge states

Rotation persists across different lattice models and geometries

Proposed spectroscopy to measure spin-quantization axis rotation

Abstract

We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin-symmetry. By considering honeycomb and square lattice realizations of topological insulators, we show that in all cases the generic behavior of a momentum-dependent rotation of the spin quantization axis is realized. Here we establish this mechanism also for disk geometries with continuous rotational symmetry. Finally, we demonstrate that the rotation of spin-quantization axis remains intact for arbitrary geometries, i.e. in the absence of any continuous symmetry. We also calculate the dependence of this rotation on the model and material parameters. Finally we propose a spectroscopy measurement which should directly reveal the rotation of the spin-quantization axis of the helical edge states.