# Graphene Brillouin Zone and Electronic Energy Dispersion

Graphene Brillouin Zone and Electronic Energy Dispersion

Graphene is a single layer of carbon atoms densely packed in a honeycomb lattice. This carbon allotropes and is the first known example of a truly two-dimensional (2D) crystal. This Demonstration considers the construction of the Brillouin zone (BZ) -bands electronic dispersion relations for a 2D honeycomb crystal lattice of graphene under the tight binding (TB) approximation. Plots are shown for the electron energy dispersion for and -bands in the first and extended Brillouin zones as contour plots at equidistant energies and as pseudo-3D representations for the 2D structures. Conventional representation of the energy dispersion relations along the lines between the high symmetry points of the first Brillouin zone is shown if you select the "usual" Brillouin zone button. You can also see the details of the dispersion curves at the hyperbolic -point (van Hove saddle point), and also around the -points with the linear energy dispersion for the two -bands (Dirac electrons), selecting "-saddle" and "-points" buttons, respectively.

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