Calculation of the energy levels of graphene Nano-discs using the semi-empirical tight-binding method

Subject Areas : Journal of Optoelectronical Nanostructures

Masoumeh Khodagholi ¹ , Bahram Bahrami ² , Zeynab Kiamehr ^{3 *}

1 - Department of Physics, Tafresh University, Tafresh, Iran
2 - Department of Physics, Tafresh University, Tafresh, Iran
3 - Department of Physics, Tafresh University, Tafresh, Iran

Received: 2025-05-28 Accepted : 2025-08-17 Published : 2025-08-25

Keywords: Semi-empirical tight-binding (TB) method, Graphene nano-disc, electronic structure, Band gap energy.,

Abstract :

In this paper, we calculate the band structure of graphene using the empirical tight-binding (TB) method in the first neighbor approximation with the SP² basis. Then, using the first-neighbor approximation SP² basis of electron and gap levels, we obtain the energy of graphene nano-discs (GNDs) with different radii. As expected, the received energy gap decreases with the increase of the radius of the nano-disc. Finally, the energy gap of a nano-disc with a very large radius converges to the energy gap in two-dimensional graphene. The numerical results show that the energy gap depends on the edges' shape and the GND's radius. Energy gap control by applying an external field is helpful in optical, infrared, and THz applications. Here, using the empirical tight-binding method for π-electrons, the effect of the external electric field on a set of nano-discs has been estimated. Applying an external electric field and its effect on the energy gap is a factor in controlling the energy gap of nano-discs.

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