Computational Investigation of Electronic Band Structure in Graphene Using Tight-binding Approximation
Abstract
Abstract Graphene is a two-dimensional allotrope of carbon arranged in a honeycomb lattice, representing a fundamental material in condensed matter physics due to its exceptional electronic properties. The electronic band structure of graphene is investigated computationally in this research. Analyzing the source of graphene's semimetallic properties and describing its low-energy electronic dispersion are the primary aims of the research. The methodology is based on constructing graphene's reciprocal lattice and computing the tight-binding Hamiltonian over a discretized Brillouin zone with a k-space grid resolution of 200 × 200 points. Three-dimensional surface plots and two-dimensional contour maps are used to depict the resulting electronic energy dispersion calculated on a two-dimensional momentum grid. The Brillouin zone's high symmetry points where Dirac cones form and govern low-energy physics receive particular attention. The conduction and valence bands meet at discrete Dirac points with a zero band gap of 0.0 eV, confirming the semimetallic nature of graphene. The energy dispersion becomes linear near these values, following the relation E = ±ℏvF|k| in the low-energy regime (|E|
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