Minimal Ingredients for Orbital Texture Switches at Dirac Points in Strong Spin-Orbit Coupled Materials

TL;DR

This paper introduces a minimal tight-binding model that explains the orbital texture switch at Dirac points in strong spin-orbit coupled materials, revealing its ubiquity and dependence on symmetry breaking and non-local effects.

Contribution

The authors develop a minimal orbital-derived tight binding model that captures the orbital texture switch at Dirac points, highlighting the key role of symmetry breaking, spin-orbit coupling, and non-local physics.

Findings

Orbital texture switch occurs in various materials with strong spin-orbit coupling.

The switch is driven by local or global inversion symmetry breaking.

The model demonstrates the ubiquity of orbital texture switches in real systems.

Abstract

Recent angle resolved photoemission spectroscopy measurements on strong spin-orbit coupled materials have shown an in-plane orbital texture switch at their respective Dirac points, regardless of whether they are topological insulators or "trivial" Rashba materials. This feature has also been demonstrated in a few materials ($\text{Bi}_2\text{Se}_3$, $\text{Bi}_2\text{Te}_3$, and $\text{BiTeI}$) though DFT calculations. Here we present a minimal orbital-derived tight binding model to calculate the electron wave-function in a two-dimensional crystal lattice. We show that the orbital components of the wave-function demonstrate an orbital-texture switch in addition to the usual spin switch seen in spin polarized bands. This orbital texture switch is determined by the existence of three main properties: local or global inversion symmetry breaking, strong spin-orbit coupling, and non-local physics (the electrons are on a lattice). Using our model we demonstrate that the orbital texture switch is ubiquitous and to be expected in many real systems. The orbital hybridization of the bands is the key aspect for understanding the unique wave function properties of these materials, and this minimal model helps to establish the quantum perturbations that drive these hybridizations.