A tight biinding calcualtion of graphene like structure

In summary, there is good agreement between the tight-binding and ab-initio calculations in the valence band of graphene, but there is a problem in the non-localized orbitals of the conduction band, particularly at the Gama (Kx=Ky=0) point in the first Brillouin zone. Suggestions for addressing this issue include including a small next-nearest-neighbor coupling in the tight-binding Hamiltonian and providing plots to further illustrate the problem. This has also been seen in hexagonal Boron Nitride.
  • #1
mohsen2002
19
0
I plot the tight binding bandstructure of graphene. There is a very good aggrement with ab-inition calculation in the valence band. but there is a problem in the non-localized orbitals of conduction band especially in the Gama(0,0) point.
Any suggestion is appreciated.
 
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  • #2
If you're comparing the results of a DFT calculation to a phenomenological nearest-neighbour tight-binding Hamiltonian then you should find that in the tight-binding band structure the conduction and valence bands are symmetric about the Dirac point (about the line E=0).

From a DFT calculation you should find that actually the two bands are not symmetric about this energy - the valence band appears to be flatter than the conduction band as far as I remember. I think this was due to the basis states not being mutually orthogonal (you should look in the Dresselhaus-Dresselhaus book on nanotubes).

If you want to reproduce the asymmetry between the two bands in the tight-binding Hamiltonian you can include a small next-nearest-neighbour coupling (say one tenth of the nearest-neighbour coupling).

If that doesn't help maybe you could just show us some plots and indicate what is wrong with them.
 
  • #3
Thanks for your reply,
The effect of next nearest neighbor on the band structure is very small. My question is:
Why the mail problem is around the Gama (Kx=Ky=0) point in FBZ?
Here is a sample fitting for hexagonal Boron Nitride. (black line are DFT result and red line as a tight binding calculation)
 

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1. What is a tight binding calculation and how does it relate to graphene-like structures?

A tight binding calculation is a computational method used in condensed matter physics to study the electronic structure of materials. It involves modeling the electronic interactions between atoms in a material to understand its properties. In the case of graphene-like structures, a tight binding calculation can help determine the band structure and electronic properties of these unique 2D materials.

2. How does a tight binding calculation differ from other methods of studying materials?

Unlike other methods such as density functional theory, a tight binding calculation does not require knowledge of the crystal structure of a material. Instead, it focuses on the electronic interactions between atoms to determine the electronic properties.

3. What are the advantages of using a tight binding calculation for studying graphene-like structures?

Tight binding calculations are computationally efficient and can provide accurate results for a wide range of materials, including graphene-like structures. They also allow for the study of electronic properties at the atomic level, providing detailed insights into the behavior of these materials.

4. Are there any limitations to using a tight binding calculation for graphene-like structures?

One limitation is that tight binding calculations typically do not account for many-body interactions, which can be important in some materials. Additionally, the accuracy of the results can depend on the specific parameters and assumptions used in the calculation.

5. How can the results of a tight binding calculation of graphene-like structures be applied in real-world applications?

The electronic properties of graphene-like structures, as determined by tight binding calculations, can have important implications for their potential use in various technologies such as electronics, energy storage, and sensing. Understanding these properties can also aid in the design and optimization of graphene-based devices.

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