About band structure calculation

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SUMMARY

This discussion focuses on the calculation of band structures using the tight binding method, specifically in the context of graphene. The user explored two approaches: one with a two-atom basis and another with a four-atom basis, leading to a Brillouin zone that is half the size of the first but with an increased number of bands. It was clarified that while using a supercell does not yield a smaller band gap, it does produce more bands, and methods exist to unfold the band structure from a supercell to retrieve the primitive cell's band structure.

PREREQUISITES
  • Tight binding method for band structure calculations
  • Understanding of Brillouin zones
  • Knowledge of supercell vs. primitive cell concepts
  • Familiarity with band gap theory in solid-state physics
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  • Research methods for unfolding band structures from supercells
  • Explore advanced tight binding models for complex materials
  • Study the implications of band structure on electronic properties
  • Learn about computational tools for band structure calculations, such as Quantum ESPRESSO or VASP
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Physicists, materials scientists, and computational chemists interested in band structure calculations and electronic properties of solids.

hokhani
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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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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.
 
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.
 

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