Graphene represents one-atom–thick layer of carbon atoms tightly packed into a honeycomb crystal lattice. Twisted bilayer graphene (tBLG), a simple vdW. Graphene Oxide (GO) water dispersion has a wide range of applications such as transparent conductive films/coatings, solar energy, bio-sensing material. Van der Waals (vdW) heterostructures -formed by stacking or growing two-dimensional (2D) crystals on top of each other- have emerged as a new promising route to tailor and engineer the properties of 2D materials. The surprising experimental discovery of a two-dimensional (2D) allotrope of carbon, termed graphene, has ushered unforeseen avenues to explore transport and interactions of low-dimensional electron system, build quantum-coherent carbon-based nanoelectronic devices, and probe high-energy physics of 'charged neutrinos' in table-top experiments. Twisted bilayer graphene: low-energy physics, electronic and optical properties. Graphene as the first truly two-dimensional crystal 7 Pseudospin, isospin and chirality of massless Dirac fermions.6 Massless Dirac fermions as low-energy quasiparticles and their Berry phase.5 Diagonalization of the tight-binding model of graphene: LCAO method.Beside brief overview of its properties, I will con-centrate on Landau levels - one of the phenomena that show extraordinary dependences due to graphene’s unusual energy dispersion. It can be efficiently used for antenna fabrication and significant benefits can be analyzed such as size miniaturization. In this seminar I present graphene, a new material with promising application possibilities and important fundamental physics aspects. 4 Tight-binding Hamiltonian of graphene One of the strongest and thinnest substances known to exist is graphene.Graphene is a single layer of carbon atoms densely packed in a honeycomb lattice. 1 Graphene as the first truly two-dimensional crystal Graphene Brillouin Zone and Electronic Energy Dispersion.

Low energy graphene dispersio