Recently I've completed an online course on thermoelectric on nanohub.org. And it's amazing, but still, some technical questions appeared. In week two, a simulation tool (nanohub.org/resources/lantrap) for calculating thermoelectric properties of materials was introduced. However, I stuck on an input format required for the simulation.
First of all, it asks for a number of bands and numbers of k-points in different directions (meaning x, y, and z) like on the attached image. Although I have no questions about the number of bands, I got pretty confused with those numbers of k-points. In electron dispersion simulation I use an 8x8x8 Mohkhorst-Pack grid that, as far as I understand, generates 512 k-points distributed throughout the Irreducible Brillouin zone. How comes that, in their example for bismuth telluride (I'm interested in the case of Bi2Te3 in particular), the number of k-points in x, y, and z directions are 19, 45, and 75. I guess the lengths of a rectangular unit cell (30.49, 7.586 and 4.38) have something to do in there, but I am not able to figure out how.
If that wasn't enough, then the input file should include nkx x nky x nkz lines (19x45x75 = 61425 in the case of tutorial example) with an eigenvalue for each line. That also confuses me. In my calculation in GPAW I use 8x8x8 grid with 200 k-points along the integration path with high-symmetry 'G', 'L', 'F', and 'Z' points for Bi2Te3, and all I get is 200 eigenvalues for each band, definitely not 60 thousand. Maybe anyone also can provide me with a clue, how to modify the code for the calclate to get something suitable for the simulation.
calc = GPAW(mode=PW(500),
xc='PBE',
h=0.10,
occupations=FermiDirac(width=0.001),
kpts={'size': (8, 8, 8), 'gamma': True},
txt='gs_Bi2Te3.txt')
a = 4.395
c = 30.44
mu = 0.399
nu = 0.206
cell = [[-a / 2, -3**0.5 / 6 * a, c / 3],
[a / 2, -3**0.5 / 6 * a, c / 3],
[0.0, 3**0.5 / 3 * a, c / 3]]
pos = [[mu, mu, mu],
[-mu, -mu, -mu],
[0.0, 0.0, 0.0],
[nu, nu, nu],
[-nu, -nu, -nu]]
G = [0.0, 0.0, 0.0]
L = [0.5, 0.0, 0.0]
F = [0.5, 0.5, 0.0]
Z = [0.5, 0.5, 0.5]
path = bandpath([G, Z, F, G, L], a.cell, npoints=200)
Kindly ask for an answer and would be glad if someone could give me some references useful to understand the math behind the generation of k-points and their eigenvalues in these type of cells since I only know the basics and it is definitely not enough to fully understand the process of the simulation.
Dear Aliaksei Bakavets I'm sorry to see that your technical question has not yet been answered by a specialist in the field. As a synthetic inorganic chemist I'm absolutely not an expert in this area. Thus all I can do is suggest to you a potentially useful research article which might help you in your analysis:
First Principles Investigations of the Atomic, Electronic, and Thermoelectric Properties of Equilibrium and Strained Bi2Se3 & Bi2Te3, with van der Waals Interactions
https://arxiv.org/pdf/1308.1523.pdf
Fortunately this paper is freely available as public full text on the internet (see attached pdf file)
Also see this relevant reference:
Enhanced thermoelectric performance of a quintuple layer of Bi2Te3
Article Enhanced thermoelectric performance of a quintuple layer of Bi2Te3
This article has not yet been posted as public full text on RG. However, four of the authors have RG profiles. Thus there is a good chance that you can request the full text directly from one of the authors via RG (if it is of interest to you).
I hope this helps. Good luck with your work!
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