Superstructures in arrays of rotated graphene layers: Electronic structure calculations

Abstract

We have applied first-principles total-energy electronic structure calculations in the local-density approximation to obtain the spatial charge density for a three-layer graphene array with the top surface rotated by $21.8\ifmmode^\circ\else\textdegree\fi{}$. It is possible to identify superstructures over the rotated layer, known as moir\'e patterns, in this system. This kind of superstructure has been reported experimentally during scanning tunneling microscopy (STM) measurements. Within this framework, we show that the simulated STM images are strongly influenced by the relative rotation of the top layer with respect to the underlying graphite. In this particular case we relate the stacking sequence of atoms to the intensity maxima at different tip-surface distances.