Local deformations and incommensurability of high-quality epitaxial graphene on a weakly interacting transition metal

Abstract

We investigate the fine structure of graphene on iridium, which is a model for graphene weakly interacting with a transition-metal substrate. Even the highest-quality epitaxial graphene displays tiny imperfections, i.e., small biaxial strains of $\ensuremath{\sim}$0.3$%$, rotations of $\ensuremath{\sim}$0.5${}^{\ensuremath{\circ}}$, and shears over distances of $\ensuremath{\sim}$100 nm, and is found incommensurate, as revealed by x-ray diffraction and scanning tunneling microscopy. These structural variations are mostly induced by the increase of the lattice parameter mismatch when cooling the sample from the graphene preparation temperature to the measurement temperature. Although graphene weakly interacts with iridium, its thermal expansion is found to be positive, contrary to free-standing graphene. The structure of graphene and its variations is very sensitive to the preparation conditions. All these effects are consistent with initial growth and subsequent pinning of graphene at steps.