Bulk-to-surface misorientation and the spin texture of topological insulators

TL;DR

This paper explores how misorientation in weak topological insulators leads to complex surface spin textures, transforming helical textures into hyperbolic ones, exemplified by Dirac-Weyl cones on SnTe's surface.

Contribution

It reveals the hidden richness of surface spin textures caused by bulk-surface misorientation in weak topological insulators, introducing a new understanding of spin texture transformations.

Findings

Misorientation induces hyperbolic spin textures.

Comparison of Dirac-Weyl cones at different points.

Surface spin textures depend on bulk-surface alignment.

Abstract

Weak topological insulators possess a symmetry related set of Dirac-Weyl cones in the surface Brillouin zone, implying misorientation between the principle axis of the low energy manifold of the bulk and the surface normal. We show that this feature of weak topological insulators comes with a hidden richness of surface spin textures, and that by misorientation a helical texture can become an unusual hyperbolic spin texture. We illustrate this effect by comparison of the $M$-point and $\Gamma$-point Dirac-Weyl cones on the (111) surface of the crystalline topological insulator SnTe.