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Graphene consists of sp2 hybridized carbon atoms arranged in a honeycomb crystal structure and connected by covalent bonds. It was first isolated in 2004 by Geim and Novoselov and has been considered a promising candidate for future nanoelectronic applications. At the low-energy limit, the charge carriers in graphene behave like massless Dirac fermions, so unusual electronic and transport properties are observed, creating a bridge between condensed matter physics and quantum electrodynamics and opening up new perspectives for carbon-based electronics. Articles that investigate both the physical properties and proposed applications of graphene are easily found in English, which is not observed in Portuguese. In this sense, this work aims to study in a systematic and didactic way the analogy between optics and electronic transport in graphene nanostructures, in particular, the focusing of an electron beam by p-n and p-n-p junctions of graphene using the tight-binding model, in order to explain concepts such as negative refraction and Veselago lens. [ABSTRACT FROM AUTHOR]

This text is a simple adaptation of the characterization via Fourier series of a class of periodic potentials to the simple cubic lattice, originally developed in the honeycomb lattice, rigorously treating both the potential type properties and the nature properties of the lattice space. [ABSTRACT FROM AUTHOR]