ABSTRACT
This chapter gives an introduction to relativity theory itself, and shows how it affects the quantum transport that we would like to understand in semiconductors. It reviews the ideas of relativity theory through the Dirac equations. The chapter discusses graphene and its band structure, with other ideas that further make it appear as a relativistic system. It also discusses the topological insulators due to their similarities to graphene. Topological insulators are materials in which a surface or interface provides a localized energy structure that has the Dirac-like bands of graphene, but generated with some additional properties. In classical semiconductors, which possess a sizable bandgap, a potential barrier higher than the energy of the incident particle generally blocks transmission of the particle through the barrier. In the Dirac bands, the eigenenergies of the Landau levels are separated by a factor that depends on the square root of the magnetic field, instead of the linear behavior in gapped semiconductors.
