  The interlayer van der Waals interaction in twisted bilayer graphene (tBLG)
induces both in-plane and out-of-plane atomic displacements showing complex
patterns that depend on the twist angle. In particular, for small twist angles,
within each graphene layer, the relaxations give rise to a vortex-like
displacement pattern which is known to affect the dispersion of the flat bands.
Here, we focus on yet another structural property, the chirality of the twisted
bilayer. We perform first-principles calculations based on density functional
theory to investigate the properties induced by twist chirality in both real
and momentum space. In real space, we study the interplay between twist
chirality and atomic relaxation patterns. In momentum space, we investigate the
spin textures around the $K$ points of the Brillouin zone, showing that
alternating vortex-like textures are correlated with the chirality of tBLG.
Interestingly, the helicity of each vortex is inverted by changing the
chirality while the different twist angles also modify the spin textures. We
discuss the origin of the spin textures by calculating the layer weights and
using plot regression models.
