On absorption spectra

[rsaniz]

Dear Yambo users,

I have carried out, succesfully I think, the calculation of the absorption spectra for SnO_2, both RPA with local field effects and excitonic. There are a couple of aspects that I am not sure how to interpret.

I find that the excitonic spectrum is basically shifted to lower frequencies with a peak weight redistribution compared tothe RPA spectrum. But there seems to be no really new peak in the spectrum. According to the threshold in both spectra, the shift is of ~0.6 eV. Is this interpretation correct? Can excitons produce a red shift of that amount without introducing new peaks in the spectrum?

Another point is that my LDA band gap is 2.5 eV. Since in experiment it is ~3.3 eV, I applied a scissors operator of 0.8 eV to my RPA spectrum. But then the RPA threshold is situated at 4.2 eV, so roughly 0.9 eV above the experimental one. Does this mean that purely electronic optical transitions between the valence band maximim and conduction band minimum are not allowed?

I'd be most grateful for any clarifications regarding the above!

Best regards,
Rolando Saniz

[Conor Hogan]

Dear Rolando,
There might be some confusion here with your meaning of the word "gap" - be careful to distinguish the "optical gap", which occurs at the onset of absorption, and the "electronic gap", which is the usual meaning of the word gap, which is given by the energy difference between top of valence and bottom of conduction band, as determined from photoemission and inverse photoemission experiments. I don't personally have any experience of SnO2, so I might not be looking at the same system as you, but a quick search on the web suggested the following numbers for bulk SnO2:
optical gap: 3.54/3.6 eV
electronic gaps: LDA: 1.7, GWA: 3.3, expt: 3.6 [from the review by Aulbur, but the original reference is not clear]
I note you give an LDA gap of 2.5eV, quite different from the one in Aulbur, you might want to look into this!

Then you quote a gap of 3.3eV. Which gap is this? The point is that the optical gap will include the red shift due to excitonic effects, so you cannot compare this directly with an LDA gap (an electronic gap), or deduce a scissors shift from this. Please have a look at these numbers, and pose your question more clearly, then we can look at the data again. Can you post the exact LDA gap at gamma (from an Abinit/PWscf run), and also post the part of the r_setup file that shows the gaps in Yambo?

An important point: being a direct gap semiconductor, the electronic and optical properties are very sensitive to the k-point grid used. Its possible, for instance, that you miss a low optical transition near gamma in your RPA spectrum, simply because you have not used a dense enough mesh, or you might even need to use an unshifted grid. Its also possible that you have dark transitions near gamma, and thats why your RPA onset is so high.

All these things depend a lot on convergence, as you can see. Besides the k-points, you might not be well converged in the BSE calculation, e.g., with the number of G vectors in the correlation. If you post your complete BSE input file that will also help.

Last point: without being too specific, its quite possible that BSE does not induce any "new" strong excitonic peak in the spectrum. There does not have to be a strongly bound exciton present. And if the quasiparticle correction is as large as 1.6eV, I think it is possible to have a renormalization as large as 0.6eV - it is about this large in bulk diamond, for instance - but lets check the gaps first.

Hope it helps!
Conor

[myrta gruning]

Dear Rolando,

in addition to what Conor said, from a quick search in the literature it seems indeed that the band gap of rutile SnO2 is optically forbidden.
E.g.
J. Phys. Chem. Solids 48, 171 (1987)

Solid State Communications
Volume 105, Issue 10, March 1998, Pages 649-652

Also in the latter from two-photon spectroscopy they determined the band gap, that is ~3.6 eV as mentioned in Aulbur review

cheers
m

[rsaniz]

Dear Conor and Myrta,

Thanks for your comments. I see better now where I am standing. Regarding the points you raise:

1. My LDA band gap is indeed lower than that of previous authors. The cause can be traced back to the fact that I used a 4 electrons pseudopotential (5s2 and 5p2), while the at least the 4d10 electrons should be included in the valence to compare with what was done before. So, my mistake.

2. The gap of 3.3 eV I quoted can be found in the original paper by Nagasawa and Shionoya [Phys. Lett. 22, 409 (1966)] reporting the series of excitonic peaks at the threshold in SnO_2 (for field perpendicular to the c axis). I was confused by a sentence in that paper stating "The fundamental absorption edge was found to begin from the photon energy of ... 3.3 eV for radiation polarized ... perpendicular to the c-axis, ..."
In any case, I was overlooking that they discuss an optical gap, which cannot be really compared with the LDA or GW gaps. I understand that.

The value of 3.6 eV in the review by Aulbur et al., who cite Palummo et al., comes from the constant in the hydrogen-like series giving the exciton energies in the Nagasawa and Shionoya paper, i.e., E_n = 3.5971 - 0.0330/n^2 (eV). Actually, in a second paper Nagasawa and Shionoya themselves indicate that the series of sharp (exciton) lines is found "near the fundamental absorption edge (3.597 eV at 1.3 K) for light polarized perpendicular to the c axis."

3. My LDA gap can be found from the (Abinit) values below; it's given by the difference between the 16th and 17th bands.

kpt# 1, nband= 32, wtk= 0.01563, kpt= 0.0000 0.0000 0.0000 (reduced coord)
-0.65462 -0.55851 -0.55851 -0.52596 -0.25273 -0.09708 -0.09708 -0.08954
-0.06466 -0.00886 -0.00759 0.02233 0.02233 0.04049 0.04049 0.07588
0.16628 0.32334 0.32334 0.32977 0.46381 0.48809 0.56085 0.56085
0.56214 0.56600 0.69042 0.69225 0.80391 0.82183 0.82183 0.82980

The gap in r_setup is

Indirect Gaps [ev]: 2.459941 7.558084
Direct Gaps [ev]: 2.459941 8.763934

So the latter coincides very nicely with the LDA one (2.459909 eV) (for my calculations I had misread this value as 2.5 eV, I apologize for that).

4. The convergence of my results with respect to number of bands and possibly other is a point I wanted to ask about. Please find below my 06_BSE file. I'd appreciate your comments.

#
# Y88b / e e e 888~~\ ,88~-_
# Y88b / d8b d8b d8b 888 | d888 \
# Y88b/ /Y88b d888bdY88b 888 _/ 88888 |
# Y8Y / Y88b / Y88Y Y888b 888 \ 88888 |
# Y /____Y88b / YY Y888b 888 | Y888 /
# / / Y88b / Y888b 888__/ `88_-~
#
# GPL Version 3.1.2 Revision 297
# http://www.yambo-code.org
#
optics # [R OPT] Optics
bse # [R BSK] Bethe Salpeter Equation.
bss # [R BSS] Bethe Salpeter Equation solver
% KfnQP_E
0.80000 | 1.000000 | 1.000000 | # [EXTQP BSK BSS] E parameters (c/v)
%
BSresKmod= "xc" # [BSK] Resonant Kernel mode. (`x`;`c`;`d`)
% BSEBands
1 | 30 | # [BSK] Bands range
%
BSENGBlk= 51 RL # [BSK] Screened interaction block size
BSENGexx= 773 RL # [BSK] Exchange components
BSSmod= "h" # [BSS] Solvers `h/d/i/t`
% BEnRange
1.00000 | 12.00000 | eV # [BSS] Energy range
%
% BDmRange
0.110000 | 0.22000 | eV # [BSS] Damping range
%
BEnSteps= 600 # [BSS] Energy steps
% BLongDir
1.000000 | 0.000000 | 0.000000 | # [BSS] [cc] Electric Field
%

Thanks so much for your time!

Rolando

P.S. I join others in expressing my sympathies to those affected by the quake.

[Conor Hogan]

Dear Rolando,
Well yes - convergence with bands is a crucial point. Just looking at the input file, I cannot tell if things are converged, of course, this you have to check yourself. BSEBands just specifies the allowed KS bands that are involved in the mixing. As you increase this value, you should see your optical spectrum converging at higher and higher energies. You can use this in tandem with BSEEhEny (needs higher verbosity I think: -V 99) which limits the e-h transition energy. for your system with 16 filled bands the range [1-30] might not be enough for the energy range you want (0-12eV?), but you need to check.

However, whats not clear to me still is if you have enough bands in the screening (BndsRnXs), which should be much higher than 30 (did you calculate the screening in a previous run?), and how you justify your scissors shift, if you have not done a GW calculation. Could you attach your r_em1s and r_optics_bse_bss files?

Cheers,
Conor

[rsaniz]

Dear Conor,

Thanks for your reply. For the moment, I have 150 bands in the screening. I still have to double-check if this is enough. I'm attaching both the r_em1s and r-06_BSE_optics_bse_bss files (tared into em1sandbss). I tried to increase the BSEands parameter to 60 to see if there is any important change in the 0-12 eV frequency range, but the job stopped without concluding. I tried a few other values and it appears I cannot set BSEbands above 32 (this is the double of the number of filled bands in my system). So I must have set something wrong at some previous stage, but I'm having a hard time trying to figure out what. My KSS file was generated with 290 bands. Perhaps the files attached have some clarifying information.

I'm not sure I understand the role of the BSEEhEny parameter. If I read well the documentation in the Yambo web site, it imposes an energy window restricting the number of bands used in the construction of the excitonic matrix, thereby reducing its dimension. I guess this saves time, but does not improve precision?

Look forward to your comments.

Best regards,
Rolando

P.S. Regarding GW, I actually did such a calculation with Abinit. Optimising the several parameters (ecuteps, ecutwfn, etc) leads to a gap of 3.84 eV. But all these calculations are with a 4 electron pseudopotential for Sn, as I mentioned in a previous posting. I'm working on a more accurate calculation, including at least the d electrons in the pseudopotential, without which the gap is known to be overestimated by GW.

[andrea marini]

I tried to increase the BSEands parameter to 60 to see if there is any important change in the 0-12 eV frequency range, but the job stopped without concluding. I tried a few other values and it appears I cannot set BSEbands above 32 (this is the double of the number of filled bands in my system). So I must have set something wrong at some previous stage, but I'm having a hard time trying to figure out what. My KSS file was generated with 290 bands. Perhaps the files attached have some clarifying information.

Dear Rolando,

in any report file Yambo writes informations about parameters of any database read/written. For example from the r-06_BSE_optics_bse_bss file you sent us I read

Code: Select all

 [RD./SAVE/s.db1]--------------------------------------------
  Bands                           :  32
  K-points                        : 21
  G-vectors             [RL space]:  7419
  Components       [wavefunctions]:  7419
  Symmetries       [spatial+T-rev]:  8
  Spinor components               : 1
  Spin polarizations              : 1
  Temperature                 [ev]: 0.000000
  Electrons                       : 32.00000
  WF G-vectors                    :  7419
  Max atoms/species               :  4
  No. of atom species             : 2
 - S/N 006804 ---------------------------- v.03.02.00 r.315 -

As you can see the number of bands are 32, and not 290. Perhaps you did something wrong in extracting the Yambo databases from the KSS file. Please check when you run a2y the number of bands reported.

Cheers

Andrea

[Daniele Varsano]

Dear Rolando,
check if you converted the right KSS database, it looks like you converted the
SCF KS structure instead of the NSCF with the higher number of bands.

Best,
Daniele

[rsaniz]

Thanks for your comments Andrea and Daniele. It turns out that in generating the KSS files I had nband and nbandkss with conflicting values in the input file (32 and 290, respectively). So I ended up with only 32 bands.

So I regenerated the KSS file with more bands, but now I have a problem with a2y. When running a2y with the new KSS file, yambo stops right away with the mssage

<---> [01] A(binit) 2 Y(ambo)
<---> Checking input file ...cassiteritexo_DS1_KSS
<---> DBs path set to :.
<---> KSS Header...At line 136 of file hdr_io.f90
Fortran runtime error: Inappropriate ioctl for device

Could this be related to the fact that I am now using a more recent version of Abinit (5.7.2)?

Thanks for your time!

Rolando

[myrta gruning]

Hallo Rolando

I did not try it out, but just looking at the source, the latest revision of Yambo should be able to read the KSS from abinit 5.7. This is not true for previous revisions like the 315 I see you are using. So I think that you need to get the latest Yambo revision (using svn see http://www.yambo-code.org/download.php)
Cheers
m