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
Graphene can be grown on ruthenium(0001) surface with CVD, temperature programmed growth (TPG) or segregation. In CVD, a hot ruthenium surface is exposed for some carbon containing molecule like methane or ethene. This results in graphene formation. It has been observed that the graphene can grow only “downhill” of the ruthenium surface steps, not uphill. 
Graphene bonds strongly with covalent bonds to the surface and has only 1.45 Å separation to the surface. This affects the electronic structure of the graphene layer, and the layer behaves differently than a free-standing graphene layer. However, the CVD graphene growth on ruthenium is not totally self-terminating and multilayer graphene formation is possible. The second and higher layers cannot bond to the existing graphene layers as strongly as the first layer bonds to the metal surface, which results in higher 3 Å separation between the graphene layers. The second layer thus has much weaker interaction with the substrate and has very similar electronic properties as free-standing graphene.
Due to the strong bonding of graphene on the ruthenium surface, only R0 orientation is observed for graphene layer. Although, different studies have shown different lengths for the moiré repeat distance, varying around Graphene(11 x 11) and Ru(10 x 10). The moiré pattern also causes strong corrugation for the graphene layer, peak height being as much as 1.5 Å.