Monolayer and bilayer graphene

This chapter presents the electronic properties of monolayer and bilayer graphene. It begins with an overview of graphene including its history, fabrication methods, properties, and current and potential applications. We then detail the tight-binding model in order to describe the emergence of the Dirac equation near the Fermi level in monolayer graphene and its consequences including massless charge carriers with a linear electronic dispersion, pseudospin and chirality, Berry phase π, Klein tunneling, and an unusual sequence of plateaus in the integer quantum Hall effect. We explain how this is generalized in Bernal-stacked bilayer graphene as characterized by a novel Hamiltonian describing massive chiral charge carriers and in AA-stacked bilayer graphene which displays two shifted copies of the monolayer bands at low energy.