Moiré Patterns of Graphene and Their Local Density of States

Abstract

Crystalline Moiré patterns have gained new interest with the discovery of two-dimensional atomically thin layers. Graphene, the most prominent example of this class of materials, is well suited to study fundamental aspects due to its inertness under ambient conditions, its well-established production and handling methods, and because of an adequate theoretical understanding of its properties. Bonding scenarios for graphene on any substrate can reach from covalent bonding to van der Waals interaction. A Moiré locally modulates the distance between the graphene layer and the substrate. The Moiré unit cell has a typical lattice constant of a few nanometers. Within the unit cell, the varying interactions of graphene with the substrate can locally modify the electronic properties of the graphene/substrate system. The first example discussed in the following is graphene (gr) on highly oriented pyrolytic graphite (HOPG). Gr and HOPG have a very similar lattice constant and Moiré patterns are produced solely by a rotation of the two lattices with respect to each other. The system is an example of the interaction of identical atoms forming a Moiré pattern. A second example with two different types of atoms and a lattice mismatch involved is chemical vapor deposition–grown gr on a Rh(111) crystal. Graphite and Rh(111) are different by their interaction strength with graphene and have been investigated by scanning tunneling microscopy (STM) and spectroscopy (STS) focusing on the Moiré pattern and its electronic structure.