The band structure of graphene is obtained from the TB approximation including only first-nearest-neighbor carbon-carbon interactions of -orbitals of a single honeycomb graphite sheet. This Demonstration calculates and plots the tight-binding (TB) electronic band structure of graphene as the 2D hexagonal carbon crystal. In solid-state physics, the TB model calculates the electronic band structure using an approximate set of wavefunctions constructed by superposition of localized atomic orbitals. The tight binding approximation (TB) neglects interactions between atoms separated by large distances-an approximation that greatly simplifies the analysis. The energy structure of crystals depends on the interactions between orbitals in the lattice. Graphene is a single layer of carbon atoms densely packed in a honeycomb lattice. 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. 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. 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. 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. This carbon allotropes and is the first known example of a truly two-dimensional (2D) crystal.
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