Decreasing number of bands in bandstructure

[Manish95]

I am plotting the bandstrucutre of monolayer MoS2 of a 4x4 supercell. I chose 10 points per segment, Bands above fermi level: automatic and default k points. I get too many bands and also not getting the direct band gap value at the K point. How to reduce the number of bands? I have attached the input file for optimization and band-structure input file. I used LCAO with GGA-PBE method with cut-off 55 Hartree. Broadening was 1000 K (I don't understand what this is?)

[Petr Khomyakov]

The band structure can be zoomed in the Band Structure Analyzer, so that you can visualize the bands around the Fermi level. The temperature of 1000 K (~80 meV) is to broaden the Fermi-Dirac distribution for the self-consistent calculations. For semiconductors and insulators this parameter should be reduced to 300 K (25 meV).

[Manish95]

How can I select DZP or HGH basis set? There is no option for these basis sets.

[Manish95]

I selected the HGH pseudopotential Tier 2 and Tier 3 for S and Mo respectively. This time I did not optimize the geometry and used the unit cell of 2H MoS2 by deleting the second layer. I increased the unit cell by 15 A on both sides (this adds vacuum ??). But still bands are flat and I don't see valley like structures. When I zoom in at K point, the bands are more or less flat.

Please help !!

[Petr Khomyakov]

Why do you leave all the band up to -60 eV? I guess you should further zoom to get your bands within something like [-5,5] eV or even smaller interval.

[Manish95]

This is what I get even after zooming. I have been trying with various combination of XC functional and basis sets. This is with LDA HGH. But I don't see the valley like structure. I don't understand why this is happening. This is for monolayer MoS2 (Supposed to give direct band gap at K point of 1.8 eV)

[Petr Khomyakov]

You have zoomed it around a very narrow k-value range for a rather broad energy interval.  I would not expect to see much of band dispersion. Why not to zoom it  in the way to see the entire band structure for all the k-intervals or at least one interval, and play a bit with the energy range. 

[Manish95]

I have tried all sorts of zoom but still can't see the valleys in the band diagram. Could you please run the input file and see?

[Ulrik G. Vej-Hansen]

Please zoom in on the full horizontal range, but a narrow vertical range and post the image here.

[Manish95]

Thanks a ton Ulrik !!
Although I still didn't get the direct band gap at K-K point of BZ, I can see the valley like structures at least. Will try other combinations of XC and basis sets.
Thanks again.

[Petr Khomyakov]

Which version of QuantumATK are you using? Did you do a band structure calculation for a primitive (1x1) cell of MoS2 to see what the band structure looks like? 

I had no problem of getting the gap at K-point for 1x1 and 4x4 cells using the latest version and pseudoDojo pseudopotential, Medium basis set, all the other parameters are set by default, and the lattice parameter as in experiment. Note that for the 4x4 supercell, the K-point of the primitive call folds onto to the K-point of this supercell Brilloiun zone, but that is in general not true for all NxN supercells of hexagonal MoS2.

[Manish95]

I am using QuantumATK 2018.06. I did my calculation with a 3 x 3 supercell. I was using plane wave DFT option with LDA and HGH pseudopotential (Tier 0 for both Mo and S). I set broadening as 300 K and wavefunction cut-off as 50 Hartree. I took a 3 x3 x 1 k space with bands per electron = 1.2.  I also increased the unit cell spacing to create a vacuum on both sides of a MoS2 monolayer. I have also optimized the geometry and then did the band structure calculation. Did you optimize the geometry or just used the experimental Wycoff positions for band structure calculation?

[Petr Khomyakov]

If you used 3x3 cell, it mean that folding is not the same as for 4x4 cell you mentioned in the very first post of yours. For 3x3 hexagonal cell, K-point of the hexagonal primitive cell is folded on the Gamma point of the 3x3 unit cell. And this is what is seen on your band structure plot. Band folding is a fully geometrical thing,not dependent on density functional, basis set, pseudopotential etc.

I would suggest reading some textbooks on Solid State Physics about how the Brillouin zone (primitive cell in the reciprocal space) is defined, in particular, reciprocal lattice vectors, how it depends on the size of the unit cell (lattice vectors) in the direct space. You may also take a look at this paper: "Extracting E versus k effective band structure from supercell calculations on alloys and impurities"
Voicu Popescu and Alex Zunger, Phys. Rev. B 85, 085201 – Published 2 February 2012.

[Manish95]

Thanks for the valuable info Petr. Just wanted ask if my supercell is 4 x 4 size, then how to we choose the appropriate k space sampling grid? I generally see in papers they use 3 x 3 x 1 or 9 x 9 x 1. So what is the apt choice of  k space sampling for a 4 x 4 MoS2 supercell.

[Petr Khomyakov]

Making a choice for k-point sampling is a matter of convergence for particular physical quantities of your interest. It does not matter whether this is a 1x1 or 4x4  unit cell. But if you know that these quantities are converged, e.g., with 12x12x1 k-grid for a 1x1 cell, then 3x3x1 k-grid is supposed to give you a similar accuracy for a 4x4 cell,  as 12/4 = 3. If the convergence is achieved with 36x36x1 k-grid for the 1x1 cell, then 9x9x1 is to be adopted for the 4x4 cell, 36/4=9. The actual choice is a matter of convergence tests for the physical quantities of interest, typically total energy, energy eigenvalues.