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General Questions and Answers / Re: Flat band and effective mass
« on: March 22, 2018, 16:04 »
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
[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
