| Description |
Consisting of a single two-dimensional layer of Carbon atoms arranged in a hexagonal lattice, graphene represents one of the most exciting recent developments in condensed matter physics. With novel electronic and mechancial properties, graphene not only has great potential with respect to technological applications, but also displays phenomena that typically appear in relativistic quantum field theory. The low-energy electronic excitations of graphene consist of two identical species of massless Dirac particles. Due to the small Fermi velocity, these particles are strongly coupled through the Coulomb interaction. Although various perturbative approaches have succeeded in elucidating many of the electronic properties of graphene, one would still like a nonperturbative study to address various questions. In particular, the spontaneous breaking of chiral symmetry in the presence of an external magnetic field, commonly known as magnetic catalysis, is one of these questions. Early studies of this phenomenon in model relativistic field theories have posited the mechanism to be universal. More recently, this mechanism of spontaneous symmetry breaking has been studied in low-dimensional condensed matter systems. Due to the strongly-coupled nature of the low-energy effective field theory of graphene, nonperturbative methods of lattice gauge theory can be used which are well suited to studying chiral symmetry breaking. Most notably used to study the theory of the strong interactions, quantum chromodynamics, these methods have proven successful in elucidating nonperturbative phenomena in cases where perturbative methods fail. In this thesis, using these methods, evidence in favor of magnetic catalysis in the graphene effective field theory will be presented. |
