Estudo do grafeno na presença de desclinações.

Abstract

Graphene is a two-dimensional crystal consisting of a hexagonal network of carbon atoms, consisting of two subnetworks. The electronic properties arise as a consequence of the linearity in the dispersion relation of the load carriers, the Dirac points. At the low-power limit, graphene can be decribed by a theory of free massless fermions, so we use the Dirac equation inWeyl’s representation in (2+1)-dimensions of space-time. In this work, we use the theory of classical elasticity, to introduce slope, in analogy with the geometric description of the curved space and the tight-binding method for a specific approach of graphene networks. We observed that the electron interacting with fermi points behaves as an effective particle (or quasiparticle) in which in the presence of the declination it acquires a phase of Berry. We consider a Riemanianna metric which represents the curved geometry of the graphene, and introduce a non-abelian caliber field due to the presence of declination. In addition, we study the influence of an external magnetic field on the energy levels of graphene. Finally, we find the analogue of the Landau levels for graphene in the presence of the defect and the external magnetic field in order to verify possible breaks in the degeneracy.