Thesis presented February 28, 2017

Abstract:
The discovery of graphene in 2004 is a two-fold breakthrough in condensed matter physics. On the one hand, its electronic properties are that of a massless Dirac fermion gas. On the other hand, its structure is the very first example of an ordered material in two dimensions. This second characteristics is studied in this thesis by scanning tunneling microscopy (STM), in the case of graphene grown in ultra-high vacuum on the (0001) surface of rhenium. In two dimensions, crystalline order is indeed impossible, and it is predicted to be replaced by a quasi-long-range order, for which the phase of the order parameter fluctuates. The rhenium substrate then acts as an outside influence that can restore crystalline order, as it forces graphene's structure to adopt an epitaxial relation with rhenium. The study of graphene's structure proposed here proves it actually originates from kinetic constraints inherited from its growth. Many typical nanostructures have indeed been identified at the atomic scale, giving access to the growth mechanism. Two reaction pathways compete. The first one gives rise to a family of metastable carbon clusters with well-defined structures in epitaxy on rhenium. The second one leads to growing graphene islands of a few nanometers in size. The coalescence of these islands and the incorporation of the carbon clusters ends up forming structural defects whose atomic structure is detailed for the first time. This exhaustive study reveals reaction pathways in the growth of graphene on rhenium are diverse, and constitute compromises between kinetics and thermodynamics. At the end of that growth, the obtained graphene is not uniform, but made of roughly 10 nm-large domains. Each domain displays a specific epitaxial relation with rhenium, in which graphene is both twisted and sheared with respect to rhenium, as revealed a STM image analysis method developed for this purpose. Elaborating a universal classification of such epitaxial relations shows they are very diverse. Two interpretations of this morphology are possible. The graphene domain walls can indeed be interpreted as topological defects in the crystalline order set in graphene by the rhenium substrate. Otherwise, they are fluctuation modes whose dynamics is frozen by the interaction with the substrate. These results put into question the notion of crystalline order set by a substrate to a two-dimensional material. They show that instead of forcing a specific epitaxial relationship, the graphene-substrate interaction gives rise to a so-called chaotic phase.

Keywords:
STM, Graphene, Quasi-Long-Range order, Topological defects

On-line thesis.