From Quantum Mechanics to Condensed Matter: Semi-Metallic Properties of Monolayer Graphene via Tight-Binding and LCAO

This literature review examines the semi-metallic properties of monolayer graphene through the theoretical approach of the Tight-Binding Model coupled with the Linear Combination of Atomic Orbitals (LCAO) method. Beyond its implications for electronics, graphene's exceptional mechanical strength, thermal conductivity, and chemical stability have positioned it as a transformative material in fields such as nanomedicine, renewable energy storage, filtration systems, and advanced composite materials. Sources from foundational quantum mechanics to contemporary condensed matter research are synthesized to trace the conceptual and mathematical bridge between atomic-scale physics to determine the electronic band structure of graphene. The analysis begins with the derivation of graphene's lattice geometry and reciprocal space, followed by a review of the formalism underlying the Tight-binding Hamiltonian. The role of LCAO in describing electron wavefunctions is explored when approximating the scaling energy factor between the energy bands in graphene, with emphasis on the presence of Dirac cones and zero bandgap behavior at the K and K′ points of the Brillouin zone, ultimately leading to the peculiar properties of graphene.