Graphene
The theory of graphene was first explored by Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Semenoff, DiVincenzo and Mele. The earliest TEM images of few-layer graphite were published by Ruess and Vogt in 1948. An early, detailed study on few-layer graphite dates to 1962 when Boehm and colleagues reported producing monolayer flakes of reduced graphene oxide. Efforts to make thin films of graphite by mechanical exfoliation started in 1990, but nothing thinner than 50 to 100 layers was produced before 2004. Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.
Graphene production techniques
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by Van der Waals forces) to retain the two dimensional electronic band structure of isolated graphene. An example of this weak coupling is epitaxial graphene on SiC and on Pt(111). On the other hand, the epitaxial graphene layer on some metals can be strongly bonded to the surface with covalent bonds. The properties of the covalently bonded graphene can differ from the ones of free-standing graphene. An example of this strong coupling is epitaxial graphene on Ru(0001). However, the coupling is strong only for the first graphene layer on Ru(0001): the second layer is more weakly coupled to the first layer and has already properties very close to the free standing graphene.