Tight Binding Hamiltonian for Graphene

[Lockoman]

Hello, I am trying to write a program that will automate the creation of a tight binding Hamiltonian matrix for armchair cut graphene. However, I have almost no experience coding and would need some help to get started.

This would be assuming that the energy between nearest neighbor carbon atoms is t and everything else zero.

The only real info I have gathered myself is that for an armchair configuration, the number of atoms along a straight x or y line will be even. (as opposed to zigzag which would be odd).

Does anyone have any tips for me or examples of this being done?

Thank you very much!

P.S. I have a copy of Maple and would ideally like to use that as opposed to matlab, mathematica, etc

 

[Nate810]

. if possible.The best way to get started with this is to look into existing implementations of tight binding Hamiltonian matrixes for armchair cut graphene, as this will give you a good starting point. You can then modify the code to suit your needs. A few good resources to check out include: - The SourceForge project "Graphene-Tight-Binding" which provides a MATLAB implementation of a tight binding Hamiltonian matrix for armchair cut graphene. - The paper "Tight-Binding Model for Graphene: A First Principles Study" by M.-H. Bae et al. which provides a detailed description of the tight binding model and how it can be used to generate a Hamiltonian matrix for armchair cut graphene. - The paper "Band Structure and Electronic Properties of Armchair Graphene Nanoribbons" by L. K. Ang et al. which uses a tight binding approach to study the band structure of armchair cut graphene nanoribbons.Hopefully these resources will help you get started with creating your own Hamiltonian matrix for armchair cut graphene!