checking the spin-orbit gap in supercell

[mcjung24]

Hi there.
I am studying the spin-orbit coupling strength of graphene.
To see the SOC strength, I am checking the energy splitting at the K-point in the DFT+SOC calculation as the unit cell size increases.

supercell size : energy gap at K-point
1x1(pristine graphene) : 1 µeV
3x3 : 12 µeV
5x5 : 75 µeV

I think that the energy splitting at the K-point should be the same regardless of the unit cell size.
However, as the unit cell size increases, the band splitting at the K-point increases.
Is this correct?

super551.zip

[manuel_engel1]

Hi,

Thanks for posting on the forum. Unfortunately, I think you meant to upload a zip archive but it didn't work. Could you please reupload the files?

When you increase the supercell size, do you keep the k-point density the same? Increasing the supercell size and increasing the k-point sampling have similar effects (in principle they should be equivalent but in practice there are usually numerical differences). So in this case, when increasing the supercell size, I would recommend to decrease the k-point grid by the same amount. Otherwise, your results will not really be comparable.

[mcjung24]

Thanks for your reply.

I have uploaded the attachment.

As you mentioned, that is true when increasing the supercell size, I need to decrease the k-point grid by the same amount.
However, I used 9x9x1 k-mesh for both calculations, because I have to have the k-point of (1/3,1/3,0) in IBZ.


I have two more questions.
1. Can I find the SOC strength of a system from VASP results?
2. In general, we define the SOC strength from the band splitting at a high-symmetry point in DFT+SOC calculation.
I believe the SOC strength should be the same for both using supercells and primitive cells, is this correct?
If so, should I divide the above values by the formula unit?

[manuel_engel1]

We do not output the SOC strength that you specified. What is written is a table of Spin-Orbit-Coupling matrix elements as detailed on the LSORBIT wiki page.

Regarding your convergence test: I would not expect to get a perfect match, and there is more settings that could influence the results. However, you could try the following: Run calculations in the way I mentioned, but with more k-points so the sampling can be reduced in the supercell:

• Unit-cell with 18x18x1 k-points
• 2x2x1 supercell with 9x9x1 k-points
• 3x3x1 supercell with 6x6x1 k-points

These calculations should be equivalent (again, in principle).

[mcjung24]

Thanks, Manuel.

When I use these parameters;
PREC=N, ISMEAR=1, EDIFF=1E-9, ECUT=520, sigma=0.2, I got a similar SOC gap of graphene.

[manuel_engel1]

That's good to hear. So the problem was probably more related to some parameters not being converged to high enough accuracy. Is your issue resolved with this?

[mcjung24]

Yes, I have solved my problem.
To get a converged result, we need to vary the parameters and check the convergence and trend.