Electronic Properties

The huge scientific and technological interest in graphene has largely been driven by its electronic properties. A good approximation to the band structure of mono-layer graphene can be obtained from a simple nearestneighbour tight binding calculation. Inspection of this band structure immediately reveals three electronic properties of mono-layer graphene which have excited such interest in this material: the vanishing carrier density at the Dirac points, the existence of pseudo-spin and the relativistic nature of carriers. In this section we aim to give an introduction to the electronic transport properties of graphene in order to highlight why it has generated so much interest. We begin by examining the band structure of graphene and discussing its implications on electron transport. We then go on to describe how to extract important material quantities such as mobility from transport measurements and proceed to introduce the more advanced topics of the quantum Hall effect (QHE), Klein tunnelling and graphene nanoribbons (GNRs). There are many fascinating transport properties, such as the fractional QHE, which we do not cover here for the sake of brevity and simplicity. The interested reader is directed towards review articles in the literature, particularly those by Castro Neto et al. (2009) and Das Sarma et al. (2011), for in-depth discussions of the transport properties of graphene.