Interpretation of elself, phdos and a2F

[chrisewolf]

Dear all!

Thanks to Carla's help I ran epw as delivered with the most recent qe6.0 running my toy model of CsPbBr3 following the GaAs example (since both are polar semiconductors...)

My point of interest is the following (I am an experimentalist): from measurement I see a dominant phonon mode of 16\pm2 meV for the broadening of the exciton line-width and now I want to find the underlying mechanism.

I run scf (k=4,4,4), ph (nq=4,4,4), epw:

nkf1 = 8 !fine electron grid
nkf2 = 8
nkf3 = 8

nqf1 = 8 !fine phonon grid
nqf2 = 8
nqf3 = 8

nk1 = 8 !nscf_epw = corresponds to the nscf
nk2 = 8
nk3 = 8

nq1 = 4 !ph.in nq1.. corresponds to the nqs list.
nq2 = 4
nq3 = 4
/
18 cartesian
0.000000000 0.000000000 0.000000000 1
0.000000000 0.000000000 0.234068700 1
[......]
-0.468137399 -0.468137365 -0.468137399 1

I am aware this is probably laughably coarse compared to literature and some examples using millions of q-points for convergence.

First I take a look at the band-structure and elself and it looks actually nice. I haven't managed mapping the elph onto the band-structure so I plot them side-by-side (see plot pdf: http://bit.ly/2eInB4T ) but clearly there is some agreement (there is a typo "sgima" in the elself output file).

then I plot the phdos and find two maxima somewhere around 14-15 meV and 20-25 meV. The first number clearly made me very happy...

when I plot a2f, there is almost no contribution at 14 meV . plot: http://bit.ly/2eTKQbs

My motivation stems from a recent paper by Wright et al. from Herz's group in Oxford (http://www.nature.com/articles/ncomms11755) and I paraphrase from there:

by comparing Im(S) with the (electron) DOS they find that when the DOS increases Im(S) increases as well. This indicates that "the increase in line-width is linked to the phase-space availability for electronic transitions".

by looking at my data it seems to indicate the same mechanism, but I wonder why there is not noticeable contribution from a2F (is this most likely a conversion problem? Some example mention ~10^5 random q-points...)

And, last but not least, why does my epw energy scale stop at the Fermi level? By plotting the full band-structure I estimated the energy scale of importance to be between -3 and 8 eV (roughly centered at the fermi energy). Then I set the window (dis_win) accordingly and selected a frozen window encompassing the fermi level (-3, 4 eV). Since I don't have any information about the orbitals i chose random projections. And I read in efermi from the scf calculation. Counting I find 8 bands within the lower level to the conduction band so I requested 8 wannier functions. A sketch is here: http://bit.ly/2dKP0Gx following the "instruction" in this paper: https://arxiv.org/pdf/0708.0650v1.pdf

Maybe someone can point me to the spot I got the input wrong?

I am glad for any comment and greatly appreciate the (free!) help!

With best wishes from South Korea

Chris

Materials Science and Engineering, POSTECH University, Pohang, South Korea

Wannier input

nbndsub = 8
nbndskip = 14
efermi_read = .true.
fermi_energy= 3.1812

wannierize = .true.
num_iter = 60
dis_win_max = 8
dis_win_min = -3
dis_froz_min= -3
dis_froz_max= 1
proj(1) = 'random'

[carla.verdi]

Dear Chris,

I am replying regarding the Wannierization first because this is the starting point of the EPW calculations: looking at the band structure plots with the various levels / windows sketched that you attached, I can see that there are 9 bands in the top valence region (between the lower blue and the red line). Hence, by requiring only 8 wannier bands you are actually wannierizing only that region (with one less band) and not the bottom of the conduction too. In order to reproduce the bands also above the Fermi level then, you should require more wannier bands (i.e. change nbndskip). As a general suggestion, you should ALWAYS plot the bands after wannierization to see that you are reproducing correctly the Kohn-Sham band structure (at least for the region of interest).

Let's see how your results change with the wannierization - however, I have a comment regarding the a2f function. This is actually well defined for metals, where you have a roughly constant density at the Fermi level, in fact see how it is calculated in Eq. (12)-(11) of https://arxiv.org/pdf/1604.03525v2.pdf
In your case I think you are just fixing the Fermi level at the top of the valence band if I am correct, hence the faction 1/N_F is not very meaningful / physically sound in this case.

Best
Carla