Confusion while doing the Band Structure calculation

Hi all

I have been trying to perform the BULK band structure calculation for Bi2Se3, after reading the Elk manual.
These were my steps:

(1) I made the crystal structure in VESTA. Bi2Se3 is rhombohedral. I selected the spacegroup R-3m, No 166 and used the hexagonal coordinate system (instead of rhombohedral). Later, I exported the data as a .cif file.

(2) Now, I used the cif2struct utility of WEIN2k to convert the file into a .struct file. This file gives the location of all the atoms in the supercell (.struct file is attached below)

(3) Having known all the atomic positions, I prepared the elk.in file with task=0 and ngridk=2 2 2 and later with task=1,20 with ngridk=10 10 10, for the cases spinorb = .true. and spinorb = .false. The elk.in file for task=1, 20, ngridk=10 10 10 and spinorb=.true. is attached below.

(4) In the above elk.in file, I have used the high-symmetry points, L (1/2, 0, 0), Z (1/2, 1/2, 1/2 ), Gamma (0, 0, 0) and F (1/2, 1/2, 1/2), from a rhombohedral RHL-1 Brillouin zone as described in this manuscript: https://arxiv.org/pdf/1004.2974.pdf .

(5) After plotting the BAND.OUT file and putting vertical lines at points given in BANDLINES.OUT, I got the band structure plots. The plots for both with and without spin-orbit coupling are attached below. Unfortunately, these plots don't look like the bulk Bi2Se3 plots elsewhere online. They seem to overlap all over and across E=0 (which is Fermi Energy according to Elk).

Can someone point out what mistake I am making? I suspect there is a mistake in selecting the k-points. Could it be that I should have selected k-points from a hexagonal Brilluion zone? I am too confused.

Last edit: Shadab Ahamed 2019-08-14

BAND.OUT

BAND_SO.OUT

Bi2Se3.cif

Bi2Se3_H.struct

bulk_NSO.png

bulk_SO.png

elk.in

J. K. Dewhurst - 2019-08-14

Hi Shadab,

I plotted your crystal structure and it doesn't look right to me.

Try to generate it again from the 'spacegroup' utility: it's easy to use.

Also, you can set

primcell .true.

in elk.in which will automatically reduce the conventional unit cell to the primitive and save you a lot of time.

Finally, if you want to enable spin-orbit coupling and you don't care about the magnetisation density, then you can use

cmagz .true.

which will make magnetism collinear in the z-direction and speed the code up considerably.

Regards,
Kay.

Shadab Ahamed - 2019-08-16

Hi John Kay Dewhurst

Thank you for your reply and help.

I am actually still in the process of learning Group Theory for understanding the physics of solids. So, I am not quite sure how to figure out things such as Wyckoff positions for the atoms in a crystal belonging to a particular space group. The spacegroup utility of Elk requires one to put Wyckoff positions in the input file so I am not very sure about how to figure out those, especially for a unit cell containing so many atoms. I tried to look at the Bilbao Crystallographic Server (http://www.cryst.ehu.es/) for help, but I cannot get my head around the information they give (or the notation they use), as of yet.

Can you explain how to figure out these Wyckoff positions for Bi2Se3, in brief, so that I can use the spacegroup utility for making the crystal? Or can you explain how to look for it on the above website for the space group R-3m, No. 166?

J. K. Dewhurst - 2019-08-18

Hi Shadab,

I've put a step-by-step HowTo for using the spacegroup code on your crystal structure here: https://sourceforge.net/p/elk/discussion/897820/thread/8c297bf308/

Regards,
Kay.

Shadab Ahamed - 2019-08-19

Thank you so much. That cleared a lot of confusion.

Shadab Ahamed - 2019-08-19

Thank you so much. That cleared a lot of confusion.

J. K. Dewhurst - 2019-08-22

Hi Shadab,

I'd like to move the discussion of Bi2Se3 back to this thread, if that's OK with you.

Here is the last point you made:

I tried doing what you said, but with no success. I made the spacegroup file with 1, 1, 3 unit cells in x, y, z direction. Later, I removed the atoms of the top unit cell; so I had one unit cell of vacuum and 2 unit cells of the material. For this, I removed 6 Bi and 9 Se atoms which had the biggest z-coordinates. I understand the length of vacuum is too large (~ 50 bohr or 28 Angstrom), but I still went with it. I wanted to do the calculation for 6 QLs and 1 unit cell of Bi2Se3 has 3 QLs, hence I wanted atleast 2 unit cells for my calculation. I still couldn't get the correct band structure. All the bands seem to lie below the E = 0 line. I am not sure where I am doing the mistake. My slurm file also has a lot of warnings which I am unable to understand.

Elk has a hard time converging vacuum regions if they are too large. You have to make the mixing parameters small enough so that the calculation remains stable. One way to do this is to include

stable .true.

in elk.in. This applies a low-pass filter to the interstitial potential and makes the Broyden mixing much less agressive. I can converge your system with this setting.

Also, upgrade to version 6.2.8 if possible: it's much faster and has better density initialisation.

I plotted your crystal structure and it probably needs to be properly relaxed to be physically correct. There will almost certainly be some surface relaxation of the atoms.

Finally, looking at your slurm file, you seem to be running with 4 MPI processes each with 4 OpenMP threads. Is this correct for your computer system? Usually we use MPI accross nodes and OpenMP on each node with OMP_NUM_THREADS set equal to the number of cores, which is a lot more than 4 these days.

Regards,
Kay.

Shadab Ahamed - 2019-09-04

Hi

Thanks for your reply. I was finally able to get a decent band structure for the surface calculation, after adding stable=.true.

But on a closer look, the two surface states are still not touching at the Gamma point. Does that mean my calculations did not really converge? Will it be better if I run with more QLs? The surface band structure and the zoomed image at gamma point is attached below.