My Community

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?

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.

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?

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).

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.

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?

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