Problem With solving the Eigenvalues of Tight Binding Method

[omaralrawi]

Dear All, this is my first post on this forum and hopefully I can get what I want. .
I am trying to build the band structure of graphene using the tight-binding method based on slater-koster correction. I use a special code to construct both Hamiltonian and overlapping matrix. I have seen when I try to diagonalize the final matrix to find the eigenvalues, the eight eigenvalues are same even if I move from Gamma- K - M. I presume there is a reason for that I don't understand it. So please I need your help to solve my issue.

 

[eljose79]

Thank you for sharing your experience with us. It is understandable to encounter some difficulties when trying to construct the band structure of graphene using the tight-binding method with slater-koster correction. As a fellow scientist, I would like to offer some insights and suggestions that may help you in solving your issue.

Firstly, it is important to ensure that your code for constructing the Hamiltonian and overlapping matrix is accurate and reliable. Any small errors in the code can greatly affect the results and may lead to the same eigenvalues regardless of the position in the Brillouin zone. I suggest double-checking your code and comparing it with other reliable sources to ensure its accuracy.

Secondly, it is possible that your code is not taking into account the symmetry of the graphene lattice. Graphene has a hexagonal lattice structure, which has a high degree of symmetry. This symmetry plays a crucial role in the band structure and can result in degenerate eigenvalues at certain points in the Brillouin zone. Therefore, it is important to incorporate this symmetry in your calculations to obtain accurate results.

Another factor that may contribute to the same eigenvalues is the size of the system you are studying. Graphene is a two-dimensional material, and the size of the system can greatly affect the band structure. If your system is too small, it may not capture the full behavior of the band structure, and hence, you may obtain the same eigenvalues.

In addition, it is worth noting that the tight-binding method is an approximation and may not accurately capture the band structure of graphene. It is always beneficial to compare your results with other methods, such as density functional theory, to ensure the accuracy of your calculations.

I hope these suggestions will help you in solving your issue. If you continue to face difficulties, I suggest seeking the guidance of a more experienced scientist or consulting relevant literature on the topic. Good luck with your research!