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.
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