Spin Orbit Effect in Graphene

[NW]

Dear ATK experts,

I calculated bandstructure of (2*2) Graphene when spin orbit interaction was considered. I considered two ways to calculate it. Firstly, I used spin polarized and defined initial spin for my calculation and then used this calculation for Noncollinear Spin Orbit (Script 1). Secondly, I used directly Noncollinear Spin Orbit calculation to obtain the bandstructure (Script 2). The results were completely different as you can see from the attached pictures.
I could not find the reason behind this difference.

[Petr Khomyakov]

In general, we advise to do self-consistent calculations with SOC included, starting from the converged spin-polarized configuration. This is what you did in Script 1.

Regarding the  second script, it might be that your calculation has not converged - using the spin-polarized solution speeds up the convergence, and this is why Script 1 makes more sense. It would be helpful to see the log files related to the 2 calculations you have done.

[NW]

Thanks Petr for your help.
I have another question. I obtained the bandgap of the structure with and without SO interaction. The bandgap value is 0.0001964eV when SOI is not considered. It then decreases to 0.0001564eV when SOI is considered. As far as I know when we consider SOI the bandgap should increase not decrease. I attached again my scripts.

[Petr Khomyakov]

For pristine graphene, you should have zero gap at the K point. In your calculations without the SOC included, you seem to get an ultra-small gap value within numerical noise or calculation error. Also, one would really have to choose a proper k-point grid, not only in terms of k-grid density - the grid should include K, M and G symmetry points, see discussion in Appendix in this paper,  Phys. Rev. B 87, 075414 (2013).

The same holds true when you include SOC, the computational settings (k-grid, mesh density and so on) must be chosen carefully. It is just my personal opinion, but this tiny SOC-induced gap in graphene does not seem to be very relevant (even at quite low temperatures), unless somebody shows me a particular example where it does.

[NW]

Thanks again for your great suggestion. I will run the previous scripts with high symmetry points.

Actually, my script is related to strained (2*2) Graphene. Because I firstly built an interface between SiC and Graphene and then remove the SiC. In this process  Graphene was under strain around 8% and I think this value of gap came from strained Graphene.

[NW]

I found that in current version of ATK, it is not possible to calculate transmission spectrum when we consider SOI. Is it possible to calculate it in the near future by ATK?

[Ulrik G. Vej-Hansen]

Which version are you using? It is possible to do in the current release, O-2018.06-SP1-1.
If you are experiencing the problem with that version, please share your script and log-file.

[NW]

I used version 2017. I should use the new one

[NW]

Is it possible to get the bandstructure in both K and K' in ATK?

[Petr Khomyakov]

You can manually specify symmetry points and the corresponding paths in the Brillouin zone for band structure calculation, see an example enclosed. 

# -------------------------------------------------------------
# Bandstructure
# -------------------------------------------------------------
def mysym():
    return {
            "G"   : numpy.array((0., 0., 0.)),
            "K"   : numpy.array((1./3., 1/3., 0.)),
            "Kp"  : numpy.array((-1./3., -1./3., 0.)),
        }

bulk_configuration.bravaisLattice().symmetryPoints = mysym

bandstructure = Bandstructure(
    configuration=bulk_configuration,
    route=['K', 'G', 'Kp', 'K'],
    points_per_segment=100,
    bands_above_fermi_level=All
    )
   
nlsave('band_structure.hdf5', bandstructure)

[NW]

Great.
Thanks a lot.

[NW]

I wanted to calculate my result with Ultra basis set, however the Spin Orbit part of my calculation did not work and I got the attached error. I did the same calculation with Medium basis set and it worked! My ATK version is 2017.1.

[Petr Khomyakov]

Please send your report about this issue to quantumatk-support@synopsys.com. Also, attach the scripts and log files related to the 2 calculations done with Medium and Ultra basis sets.

[NW]

To obtain the best results for SOC, is it better to define InitialSpin or RandomSpin in the script?

And can I use RandomSpin for spinpolarized calculation and then use it as a old calculation for non-collinear Spin Orbit?

[Petr Khomyakov]

To obtain the best results for SOC, is it better to define InitialSpin or RandomSpin in the script?

I do not know what "the best results" mean in this case. You may do the calculations with these 2 options and choose the result that suites you best.

And can I use RandomSpin for spinpolarized calculation and then use it as a old calculation for non-collinear Spin Orbit?

In principle, you can use any "old calculation" as an initial guess. Whether this is a good guess or not is a matter of numerical experiment.