Topological electronic phases in graphene

Abstract

Graphene is a two dimensional material made of single layer of carbon atoms arranging into a honeycomb lattice. It can be synthesized by variety of methods as exfoliation, chemical vapor deposition or organic polymerization. Its electronic properties are not the ones of an insulator nor a metal, being usually known as a zero gap semiconductor. Electrons in graphene behave as massless Dirac fermions, having a zero effective mass. The Dirac equation that governs electrons turns graphene into a material that can easily develop topological states due to Berry phase effects of the Dirac points. Such topological states of matter are characterized for having properties which are independent on the defects and imperfections that the material might have. The two dimensional nature of graphene makes it specially suitable to inherit properties from other materials by proximity effect, as superconductivity or magnetism. In this thesis we will explore by means of theoretical techniques how graphene can show topological insulating states by combination of magnetic fields, electron-electron interaction, spin orbit coupling, exchange and superconducting proximity effects.