Advanced Considerations on the Electronic Dispersion Relation of Graphene

It is through study of the QHE that we can directly observe the requirement to treat the electrons in graphene using the Dirac equation, as massless relativistic particles. We will begin with a general description of the classical and QHEs, before moving on to the anomalous QHE in graphene. Readers already familiar with the classical Hall effect may therefore wish to skip to Section 4.1.2, and readers familiar with the QHE may wish to skip to Section 4.2.