Graphene is an allotropic form of carbon made by a monolayer of carbon atoms arranged in a honeycomb crystalline lattice. It can be experimentally obtained through the use of several methods, being the exfoliation of graphite the easiest way. Graphene can be considered the first genuinely two-dimensional material, since it is constituted of a single atomic layer, in contrast to several material structures, such as thin films, which behave as two-dimensional ones, due to the fact that one of the three space dimensions is highly reduced in comparison to the others, but still consisting of many atomic layers. The most striking theoretical prediction, experimentally confirmed, is that electrons in graphene behave as massless Dirac fermions in a “relativistic” (1+2)-D space-time, consisting of one temporal dimension and two space dimensions, near the so-called Dirac points, opening the possibility of emulating high-energy physics through the use of a low-energy condensed matter system, beside the promise to revolutionize the high-speed electronics. The aim of the present contribution is to put forward the fundamentals of Dirac fermions, explaining how the effective model emerges in graphene. We understand that there is a poor literature on the subject in Portuguese. Also, graphene provides a useful introduction to relativistic field theory and to the second quantization methods.
Keywords:
graphene; Dirac equation; Dirac fermions
