From Quantum Mechanics to Condensed Matter: Semi-Metallic Properties of Monolayer Graphene via Tight-Binding and LCAO
DOI:
https://doi.org/10.58445/rars.3099Keywords:
graphene, monolayer graphene, band structure, dirac semimetal, LCAO, Tight-Binding, Quantum Mechanics, Condensed Matter Physics, Electronic Properties, 2D materialsAbstract
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.
References
Le Hur, K., & Al Saati, S. (2023). Topological nodal ring semimetal in graphene. Physical Review B, 107(16), 165407. https://doi.org/10.1103/PhysRevB.107.165407
Chu, J. (2023, January 30). Study: Superconductivity switches on and off in “magic‑angle” graphene. MIT News. Retrieved from https://news.mit.edu/2023/study-superconductivity‑switches‑and‑off‑in‑magic‑angle‑graphene‑0130
Zhang, F., Sahu, B., Min, H., & MacDonald, A. H. (2010). Band structure of ABC‑stacked graphene trilayers. Physical Review B, 82(3), 035409. https://doi.org/10.1103/PhysRevB.82.035409
Zhang, X., Zhang, Y.-H., Calder, S., Hallas, A. M., He, W.-Y., ... & Dai, P. (2025). Competing superconductivity and charge density waves in a kagome metal. Physical Review Letters, 134(15), 150001. https://doi.org/10.1103/PhysRevLett.134.150001
Mealing, P. P. (2011, May 24). Trying to understand Schrödinger’s equation. Journeyman Philosopher. Retrieved [today’s date], from https://journeymanphilosopher.blogspot.com/2011/05/trying-to-understand-schrodingers.html
Anosh, A., & Sirat, S. A. (2024). An overview of the electronic structure of monolayer graphene. Journal for Research in Applied Sciences and Biotechnology, 3(2), 39–44. https://doi.org/10.55544/jrasb.3.2.10
Baidak, S. T., & Lukoyanov, A. V. (2023). Semimetallic, half-metallic, semiconducting, and metallic states in Gd–Sb compounds. International Journal of Molecular Sciences, 24(10), 8778. https://doi.org/10.3390/ijms24108778
de Martino, A., Dell’Anna, L., & Egger, R. (2007, February 6). Magnetic confinement of massless Dirac fermions in graphene. Physical Review Letters, 98, 066802. https://doi.org/10.1103/PhysRevLett.98.066802
Utermohlen, F. (2018, September 12). Tight‑binding model for graphene. Retrieved from https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/3/67057/files/2018/09/graphene_tight‑binding_model‑1ny95f1.pdf
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