The amazing graphene: an educational bridge connecting different Physics concepts

The purpose of this work is to present a learning workshop covering various physics concepts aimed at strengthening physics/engineering student understanding about the remarkable properties of two dimensional materials, graphene in particular. At the basis of this learning experience is the idea of blending and interconnecting separate pieces of knowledge already acquired by undergraduates in different courses and to help them visualize and link the concepts lying beyond separate chunks of information or equations. Graphene represents an appropriate unifying framework to achieve this task in view of its monatomic structure and various exotic processes peculiar to this and some other two dimensional crystals. We first discuss essential elements of group theory and their application to the symmetry properties of graphene with the aim of presenting to physics/electronic engineering undergraduates that in a system characterized by symmetry properties such as a crystal, the acquisition of the solutions of the Schrödinger equation is simpler and easier to visualize than when these properties are ignored. We have then selected and discussed some remarkable properties of graphene: the linear electron energy-momentum dispersion relation in proximity of some edge points of the Brillouin zone; the consequential massless Dirac behaviour of the electrons; their tunnelling behaviour and the related Klein paradox; the chiral behaviour of electrons and holes; the fractional quantum Hall effect in massless particles; and the quantum behaviour of correlated quasiparticles observable at macroscopic level. These arguments are presented in a context covering related pieces of knowledge about classical, quantum and relativistic mechanics. Finally, we mention current applications and possible future ones with the aim of providing students with an expertise that could be useful for further work experiences and scientific investigations regarding new materials, having farreaching implications in various fields such as basic physics, materials science and engineering applications.