  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.
