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This paper explored the electronic properties of the graphene sheet and also developed basis for understanding the electronic properties of the curved graphene sheet. This paper began with setting up basic knowledge about solid-state physics including introducing band structure, band gap, crystal structure, and reviews for quantum mechanical operators. Then this paper described two potential models that are suitable for considering periodic potential: the weak potential and the tight-binding model. We discovered the tight-binding model is better for our graphene case and by applying this model we find the energies of the graphene sheet. Next, we constructed the 1D and 2D Hamiltonian matrix in python with periodic potentials and plotted the energy levels and wave functions. Finally, this paper touched on gaussian curvatures and two possible shapes for graphene to be curved.
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Yanpei, Deng, "Electronic Properties of Flat and Curved Graphene Sheets" (2021). Senior Projects Spring 2021. 203.
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