Number of lines in Band Structure

[chow_dhury]

TL;DR Summary

How many lines should there be in Band Structure from DFT calculation?

The general idea is that, number of bands=number of lines.
For instance, AlAs primitive cell (one of each atom per cell) has 13 bands; that is outer most shells have 13 distinct energy values. (Al: one 3s + three 3p, As: five 3d + one 4s + three 4p)

But when I calculate Band Structure through CASTEP, i could count 17/18 lines.
How does that make sense?

Note: It has 18 electrons in those shells.

 

[eljose79]

Thank you for sharing your observation about the discrepancy in the number of bands and lines in the band structure of AlAs. I would like to offer some possible explanations for this difference.

Firstly, it is important to note that the number of bands in a material's band structure is not always equal to the number of lines. This is because the band structure is a representation of the electronic energy levels of a material, and it takes into account both occupied and unoccupied energy levels. On the other hand, the number of lines that can be observed in a band structure plot is determined by the number of energy levels that are occupied by electrons.

In the case of AlAs, the primitive cell has 13 bands, as you have correctly stated. However, the total number of electrons in the system is 18, which means that some of the energy levels will be occupied by more than one electron. This can result in the observation of more lines in the band structure plot than the number of bands in the system.

Another factor that can contribute to the difference in the number of bands and lines is the use of different methods for calculating the band structure. In your case, you have used CASTEP, which uses density functional theory (DFT) to calculate electronic structures. DFT is a powerful tool, but it is not exact and relies on approximations. Therefore, the results obtained may not always match the expected values.

Lastly, it is also possible that the band structure plot you have obtained may include some phonon modes or spin-orbit coupling effects, which can also contribute to the number of lines observed.

In conclusion, the discrepancy between the number of bands and lines in the band structure of AlAs can be explained by considering the electronic occupancy, the approximations used in the calculation, and the presence of other effects such as phonons and spin-orbit coupling. I hope this helps to clarify your doubts.