spectral function normalization

[Nikita Rybin]

Hello, @stepan-tsirkin!

I have a small question related to the normalization of the spectral function. When we use "density" option for plotting, the spectral function has intensity, which is not from 0 to 1. In my understanding, this is not a scaling issue (cause in principle, we can scale intensities from [0,x] to [0,1]), but it is related to the normalization of the spectral function when the delta function is presented as gaussian in the code. Am I right that if the spectral function is properly normalized it should be between 0 and 1 or I am missing something? Could you, please, clarify this point?

[Stepan Tsirkin]

Hi @NickRybin ,

No, the densitydoes not have to be between 0 and 1. When a delta-function is represented by a gaussian, the integral should be fixed, not the value at maximum.

[Stepan Tsirkin]

@NickRybin

More detailed : If a band is represented as a gaussian (or any other smeared peak) g(E) it should be

\int g(E) dE=1

but when doing unfolding, that gaussian is multiplied by the unfolding weight W, which is between 0 and 1. But if 2 or more bands are degenerate (within the threshold), then the weights add up, so the weight may be actually greater than 1.

Does it answer your question?

[Nikita Rybin]

Hi, Stepan!

Yeap, this I understand, but then I calculate degeneracy wrongly. I have Si supercell (at equilibrium, i.e. zero temperature, no distortion, so all the weights should be either 0 or 1) and for some reason the valence band maxima has an intensity ~6, whereas I though that the VBM at gamma point is three fold degenerate and shold have intensity ~3. The same I observe for the CBM at Gamma point, where the degeneracy, as I count should be 3, but somehow the intensity is also ~6.

UPDATE: spin ...

[Stepan Tsirkin]

Hi Nikita,

Yes, if you do a spinor calculation, the deeneracy is 6. The deeneracies are easier to see in the weights, e.g. here :

banduppy/tutorial/reference/bandstructure_unfolded.txt

Lines 476 to 503 in f26af6a

 1.002099092323117890e+00 -5.672868818000618596e+00 9.999999993771073736e-01 
 1.002099092323117890e+00 -1.530748999540801236e+00 6.507842698755263753e-10 
 1.002099092323117890e+00 -1.530604380002926757e+00 1.062156130836447783e-10 
 1.002099092323117890e+00 3.385296268939047337e+00 1.914193609995768699e-09 
 1.002099092323117890e+00 6.230540974609525051e+00 2.999999997229518378e+00 
 1.002099092323117890e+00 6.966684983507025031e+00 3.306559579257887464e-09 
 1.002099092323117890e+00 8.804745930974899437e+00 2.999999997668295393e+00 
 1.002099092323117890e+00 9.702591190822339229e+00 9.999999995368966665e-01 
 1.002099092323117890e+00 1.396004482000723712e+01 1.999999999488396796e+00 
 1.002099092323117890e+00 1.424180986343413302e+01 9.999999999245685611e-01 
 1.002099092323117890e+00 1.635788694525850318e+01 4.003529700518522753e-09 
 1.002099092323117890e+00 1.721047151814454068e+01 1.262042982258099629e-09 
 1.002099092323117890e+00 1.750696057620226043e+01 2.999999994548078419e+00 
 1.002099092323117890e+00 1.878209547909183996e+01 2.625850332418585542e-09 
 1.002099092323117890e+00 -5.672868818000618596e+00 9.999999993771073736e-01 
 1.002099092323117890e+00 -1.530748999540801236e+00 6.507842698755263753e-10 
 1.002099092323117890e+00 -1.530604380002926757e+00 1.062156130836447783e-10 
 1.002099092323117890e+00 3.385296268939047337e+00 1.914193609995768699e-09 
 1.002099092323117890e+00 6.230540974609525051e+00 2.999999997229518378e+00 
 1.002099092323117890e+00 6.966684983507025031e+00 3.306559579257887464e-09 
 1.002099092323117890e+00 8.804745930974899437e+00 2.999999997668295393e+00 
 1.002099092323117890e+00 9.702591190822339229e+00 9.999999995368966665e-01 
 1.002099092323117890e+00 1.396004482000723712e+01 1.999999999488396796e+00 
 1.002099092323117890e+00 1.424180986343413302e+01 9.999999999245685611e-01 
 1.002099092323117890e+00 1.635788694525850318e+01 4.003529700518522753e-09 
 1.002099092323117890e+00 1.721047151814454068e+01 1.262042982258099629e-09 
 1.002099092323117890e+00 1.750696057620226043e+01 2.999999994548078419e+00 
 1.002099092323117890e+00 1.878209547909183996e+01 2.625850332418585542e-09 

I see only upto 3-fold degeneracies, but that is a scalar calculation.

[Nikita Rybin]

Yes, you are right! I completely forgot about the spin. Thanks for clarifications.