[QE-users] k-points and path for Band structure calculation

[Giovanni Pizzi]

Dear Chaman,

1. Yes. Actually, the band paths are just conventions, and try to pass through all points and lines that have some symmetry.
So, the “suggested” band paths depend a lot on the lattice (and actually also, in some cases, on the space group, if you want to cover all inequivalent lines, as we discuss in [1]).

The band structure is not affected by the path you choose (but of course, by choosing a different path, you’ll see different bands).

2. It’s up to you. The ones of wikipedia cover a more complete path, but in many cases the relevant features (e.g. lowest conduction band, highest valence band, …) might only appear for a given material along a subset of the lines, so you can decide show show less paths if you know the material and what you are doing.
If you are unsure, I suggest to use our seekpath tool at https://www.materialscloud.org/work/tools/seekpath - this will also standardise the cell and check the spacegroup symmetry, and e.g. distinguish between hP1 and hP2 (the path that you/wikipedia report is for what we call hP2; hP1 needs an additional segment K-H_2 that is for some space groups is not equivalent to K-H; our paper [1] explains more about this).

3. I don’t know. In general they use a shorter path and this is OK. The only thing that I’m not sure about is what is the U point for them, as this is not a standard point for a hexagonal cell. I didn’t have the time to check the paper to see if they say what U is. However, note that at U most bands do not have extrema (only one band has a minimum).

So my guess, now that I look better at it, they might be just refolding the band structure and using the names of the letters from the cubic FCC lattice, refolded on the hexagonal lattice, and this might explain the U point (that exists in cF lattices).

However, to confirm this, you will need to check the refolding and try to reproduce the band structure, to know if this is the correct interpretation (or check if they explain more in the paper).

Hope this helps,
Giovanni Pizzi


[1] Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, I. Tanaka, Band structure diagram paths based on crystallography, Comp. Mat. Sci. 128, 140 (2017). DOI: 10.1016/j.commatsci.2016.10.015<http://doi.org/10.1016/j.commatsci.2016.10.015>


--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi

On 26 May 2020, at 17:15, Chaman Gupta <chaman at uw.edu<mailto:chaman at uw.edu>> wrote:

Hey everyone,

I am trying to study the effect of pressure on the band structure of 'Si - simple hexagonal (Phase V)', which is stable between 17 to 30 GPa (approx.)

Here is a paper published in Nature (https://www.nature.com/articles/s41586-020-2150-y), which has a figure with the band structure of Hex-Si (image is attached). The image has the following path  " A - Gamma - M - U - L ".

IMAGE 1 IS HERE<https://drive.google.com/file/d/1zaJSjv3RX3gy87NTuBV5AjkJysW7pdOZ/view?usp=sharing>

When I looked for BZ1 and the path to take for a simple hexagonal structure, I came across this link ( https://en.wikipedia.org/wiki/Brillouin_zone). It mentions the path to be "Gamma - M - K - Gamma - A - L - H - A|L - M|K - H"

My questions:

1. From what I understand, the path and symmetry points are dependent on the type of lattice, and highly affect the band structure. Is this statement right or wrong?

2. Which k-points/ High symmetry points/ BZ1/ path should I use for my band structure calculation?

3. Is it possible, by any chance the author of this Nature paper, might have used the wrong k-points? Or should I use what they have used?

Thanks for the help.


Regards,

Chaman Gupta
Graduate Research Student, Novosselov Research Group<http://depts.washington.edu/nrglab/>, UW
Graduate Research Student, Pauzauskie Research Group<https://depts.washington.edu/pzlab/wordpress/>, UW
University of Washington Seattle, M.S. in Mechanical Engineering
IIT Kharagpur, B.Tech in Metallurgical and Materials Engineering
Linked In<https://www.linkedin.com/in/professorchamangupta> | Email<mailto:chaman at uw.edu> | P: +1 (206) 383-3514
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