Flat band and effective mass

[aryt13]

I have this very flat CBM between M and K. I am trying to calculate the effective mass at K, but I get 0.772. That can't be correct or am I missing something here?

[Jess Wellendorff]

Are you calculating the effective mass along the correct/expected direction? (in the M-K direction in reciprocal space)

[aryt13]

Thanks for the reply Jess. To be honest I don't quite understand how direction works in VNL. Is it supposed to be in form of a vector or is it a point in the desired direction? Anyhow, I tried with a few different directions and I got pretty much the same results:

[0.3, 0.35,0] => 0.772
[0.24, 0.24, 0] => 0.775
[0, 0.5, 0] => 0.772

*Fractional coordinates

One reason could be because the CBM in the K-Gamma portion, unlike the M-K portion, is not flat and since VNL uses a central finite difference (I guess?), then the result is inaccurate. So I tried to use the equation in this tutorial (https://docs.quantumwise.com/tutorials/effective_mass/effective_mass.html) to calculate the effective mass manually, but the numbers do not make any sense. I obtained the second derivative at the K point using Origin Pro. My idea was to use the curve derivative slightly toward M and slightly toward G point to get the values for M-K and K-G . Then I plugged it in the equation and the numbers are just too small. I'm not sure if I'm using the right units for the reduced Planck constant and the electron rest mass. Is hbar 6.582x10^-16 eV.s?

In case you are wondering, when you zoom in the M-K portion, here's how the CBM looks like. The M-K portion has a very slow slope while the G-M and K-G portion have a very sharp slope.



And here's the raw data:

0.3084   3.9775
0.3277   3.66
0.347   3.4497
0.3663   3.3755   <= M-Point
0.3855   3.3809
0.4047   3.3963
0.4239   3.42
0.4431   3.449
0.4623   3.479
0.4815   3.5044
0.5007   3.5191
0.5199   3.5181
0.5391   3.5012
0.5583   3.4766
0.5775   3.4627    <= K-Point
0.5967   3.4859
0.6159   3.5674
0.6351   3.7177

[Petr Khomyakov]

The special/symmetry k-points are set as a list in the Band structure analysis object. The corresponding symmetry lines are just intervals between these points, e.g., setting G, M, K, A means that the band structure will be calculated for the G-M, M-K and K-G lines. The defaults are set in the Band structure analysis object, based on the Bravais lattice set in the Builder for the structure of study.   

It might be helpful to see your python script to get an idea of what you are actually trying to do.