Using the tight-binding model to derive a dispersion relation for graphene energy

Authors: Mosin M.A.
Published in issue: #4(9)/2017
DOI: 10.18698/2541-8009-2017-4-77
Category: Informatics, Computer Engineering and Control | Chapter: System Analysis, Control, and Information Processing, Statistics
Keywords: carbon nanotubes, graphene, graphene conductivity, tight-binding model, dispersion relation for energy, Bloch functions, Brillouin zones, Dirac points
Published: 10.04.2017

We solve the problem of accounting for varying graphene-based nanostructure parameters by means of conducting numerical simulations. To solve the Schrödinger equation, we used the tight-binding model as an alternative to molecular dynamics simulation. We describe implementing this method for the case of π electrons in a graphene layer. We derive a dispersion relation for graphene energy. It is possible to use the results presented to determine the band structure of single-walled carbon nanotubes and to study their electronic properties.

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