Electronic properties and van Hove singularities of observed moir{\'e} patterns of dislocated graphene on HOPG

Highly Oriented Pyrolitic Graphite (HOPG) can be described as stacked graphene layers. Due the weak van der Waals interaction between the layers, topmost layer of HOPG can be rotated or shifted by chemical or mechanical means. With rotation of the topmost layer, super periodic structures called as moir{\'e} patterns are formed. In this work, moir{\'e} patterns on HOPG surfaces due to dislocated graphene layers were studied. A simple geometric investigation of the atomic structure of the moir{\'e} patterns revealed that different atomic moir{\'e} periodicities result in similar geometric moir{\'e} periods. Our calculations showed that the band structure of moir{\'e} patterns even though exhibits the fingerprints of those of twisted bilayer graphene system, like the preserved Dirac cone at the K point of moir{\'e} Brillouin zone, it has several new emerging features like van Hove singularities and linear or flat bands depending on the moir{\'e} periodicity. Our results show that most of the moir{\'e} patterns observed on graphene/HOPG system do not have a purely electronic or structural origin, but both. Moreover, our results show that van Hove singularities in these systems with different twist angles have different origins in their respective band structure.