Scattering in Bernal stacked tri-layer graphene
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In this thesis we characterize multi-layer graphene within the tight-binding model and compute the low energy band structure to reveal the nature of particles situated at the Dirac points. We also address the problem of scattering through a localized impurity located on the surface of a tri-layer graphene system and focus on the modulations it induces on the two surfaces. We approach this problem within the framework of a T-matrix formalism, both numerically and analytically, which encases all possible scattering events thus enabling a realistic description of impurity scattering. We find that the impurity induces Friedel oscillations that decay with 1 r in graphene with more than one layer. The modulations are then analyzed in momentum space where we find that Bernal (ABA) stacked tri-layer graphene has specific characteristics that allow it to be distinguished from rhombohedral (ABC) tri-layer graphene. Experimentally these properties can be imaged directly from scanning tunneling microscopy.