Moir\'e patterns on STM images of graphite from surface and subsurface rotated layer

We have observed with STM moir\'e patterns corresponding to the rotation of one graphene layer on HOPG surface. The moir\'e patterns were characterized by rotation angle and extension in the plane. Additionally, by identifying border domains and defects we can discriminate between moir\'e patterns due to rotation on the surface or subsurface layer. For a better understanding of moir\'e patterns formation we have studied by first principles an array of three graphene layers where the top or the middle layer appears rotated around the stacking axis. We compare the experimental and theoretical results and we show the strong influence of rotations both in surface and subsurface layers for moir\'e patterns formation in corresponding STM images.