About band structure calculation

In summary, the conversation discussed the use of graphene and the tight binding method to solve for energy dispersion. Two different approaches were mentioned - one with two basis atoms and the other with four. It was noted that the second approach resulted in a Brillouin zone half the size but with a larger number of bands. The question was raised about the correctness of this approach in studying electronic properties of solids, as it may lead to a smaller band gap in insulators. It was clarified that while there may be more bands, there are methods to unfold the band structure and retrieve the primitive cell. The conversation ended with the confirmation that bringing states outside of the smaller first Brillouin zone inside results in new bands.
  • #1
hokhani
483
8
My question is more general but I explain it by a simple example i.e. graphene and tight binding method. I solved energy dispersion of graphene with tight binding by the two ways: First, I took graphene as a lattice with the two basis atoms A and B. In the second way, I took graphene as a lattice with four atoms, the two A and the two B atoms. In other words, I took the two unit cell as one and solve the problem. As expected, in the second way, I obtained a Brillouin zone half the first one but with larger number of bands. I don't know whether or not this approach is correct in treating the electronic properties of solids. Because for example using the second way in the insulators we may obtain the smaller gap for the insulator so that the material may no longer be an insulator! Could anyone please help me with that?
 
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  • #2
You will not get a smaller band gap, but certainly you will get more bands as you mentioned. There is nothing wrong in calculating the band structure for a supercell rather than the primitive cell.

In fact there are methods to unfold the band calculated using a supercell to retrieve the band structure of the primitive cell.
 
  • #3
Useful nucleus said:
You will not get a smaller band gap, but certainly you will get more bands as you mentioned. There is nothing wrong in calculating the band structure for a supercell rather than the primitive cell.

In fact there are methods to unfold the band calculated using a supercell to retrieve the band structure of the primitive cell.
Ok. Thanks. Bringing the states which are out of the smaller FBZ inside, results in new bands.
 

1. What is band structure calculation?

Band structure calculation is a theoretical method used to understand the electronic properties of solids. It involves calculating the energy levels and corresponding wave functions of electrons in a material, which determine its electronic and optical properties.

2. Why is band structure calculation important?

Band structure calculation is important because it helps us understand the behavior of electrons in a material, which is crucial for predicting its properties and potential applications. It also provides insight into the fundamental physics of materials, and can aid in the design and development of new materials with desired properties.

3. What factors affect the accuracy of band structure calculations?

There are several factors that can affect the accuracy of band structure calculations, including the choice of theoretical model, the size of the system being studied, and the computational methods used. Additionally, the accuracy may also be affected by the level of approximation and the quality of the input data.

4. How are band structure calculations performed?

Band structure calculations are typically performed using computer simulations and mathematical models, such as density functional theory (DFT) or tight-binding (TB) methods. These methods involve solving the Schrödinger equation for the electrons in the material, taking into account the interactions between them and the periodic potential of the crystal lattice.

5. What are some applications of band structure calculations?

Band structure calculations have a wide range of applications in materials science, condensed matter physics, and other fields. They are used to study the electronic properties of semiconductors, metals, and insulators, and to predict the behavior of materials under different conditions. They are also important for understanding and designing electronic and optoelectronic devices, such as transistors, solar cells, and LEDs.

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