Excitonic effects in metallic systems ?

[Yunfeng]

Dear All,

First, many thanks to Andrea and Myrta for valuable explanation on metal systems. Now I have some new questions.

For metals, an accepted routine is to split the dielectric function into the intraband contribution, which is cast in the form known from the Drude free electron theory, and the interband contribution [J. Phys. Condens. Matter. 19, 196105 (2007)]. Does Yambo indeed calculate the interband contribution only or altogether (both interband and intraband)?

If only the interband contribution is caclulated, the dielectric function should not diverge in the long wavelength limit. In fact, only another part from Drude free electron lead to diverge for ideal metal. Am I right? If yes, the BSE equation in principle should work, no matter that the system has excitonic effects or not (I mean in principle, we should not forbid/disallow this kind of calculations in the code. ). Am I right? Another question: do you expect some difference on the calculated spectra on q--->0 (yambo -b -o b -y h and change 'xc' to 'x' in yambo.in) and q=0 (yambo -o c)? If yes, what's the physics behind?

Now let's forget about the BSE instead using RPA. I have done a test calculation on the optical spectra of Aluminum , which is well-established both from experiment and theory [Phys. Rev. B 3, 1898 (1971) and Phys. Rev. Lett. 25, 156 (1970)]. But unfortunately I didn't obtain a nice spectrum, that is, the first peak is rather strong than the previous calculations and experiments.

yambo.jpg

siesta.JPG

Well, comparing with your paper on cooper and silver [Phys. Rev. Lett. 91, 176402 (2003)], they both are not very good in terms of the absolute value. But now we even didn't obtain a good curve in terms of relative intensity . The input files are attached below:

Al.scf.in

&control
calculation='scf'
restart_mode='from_scratch',
prefix='al'
tprnfor = .true.
tstress = .true.
pseudo_dir = '/home/liang/PP/' ,
outdir = '/localscr/liang/tmp/Al/'
/
&system
ibrav= 2, celldm(1) =7.62, nat= 1, ntyp= 1,
ecutwfc =30.0,
occupations='smearing', smearing='marzari-vanderbilt', degauss=0.05
/
&electrons
diagonalization='david'
mixing_mode = 'plain'
mixing_beta = 0.7
conv_thr = 1.0d-8
diago_full_acc = .true.
/
ATOMIC_SPECIES
Al 26.98 Al.pbe-rrkj.UPF
ATOMIC_POSITIONS
Al 0.00 0.00 0.00
K_POINTS { automatic }
18 18 18 0 0 0

Al.band.in

&control
calculation='bands' ,
wf_collect = .true. ,
prefix='al' ,
pseudo_dir = '/home/liang/PP/' ,
outdir = '/localscr/liang/tmp/Al/'
/
&system
ibrav= 2, celldm(1) =7.62, nat= 1, ntyp= 1,
ecutwfc =30.0, nbnd = 150,
nosym = .false.
/
&electrons
diagonalization='cg' ,
diago_thr_init = 1.e-8 ,
diago_full_acc = .true. ,
/
ATOMIC_SPECIES
Al 26.98 Al.pbe-rrkj.UPF
ATOMIC_POSITIONS
Al 0.00 0.00 0.00
K_POINTS { automatic }
18 18 18 0 0 0

yambo.in

optics # [R OPT] Optics
chi # [R CHI] Dyson equation for Chi.
% QpntsRXd
1 | 1 | # [Xd] Transferred momenta
%
% BndsRnXd
1 | 150 | # [Xd] Polarization function bands
%
NGsBlkXd= 1 RL # [Xd] Response block size
% EnRngeXd
0.00000 | 10.00000 | eV # [Xd] Energy range
%
% DmRngeXd
0.02000 | 0.80000 | eV # [Xd] Damping range
%
ETStpsXd= 500 # [Xd] Total Energy steps
% LongDrXd
1.000000 | 0.000000 | 0.000000 | # [Xd] [cc] Electric Field
%

Sincerely, Yunfeng

[myrta gruning]

Dear Yunfeng,

about the relative intensity of the peaks, it very much depends on the broadening one applies to the spectrum.
In your case you have chosen

% DmRngeXd
0.02000 | 0.80000 | eV # [Xd] Damping range
%

That means that the broadening varies linearly from 0.02 to 0.8 eV in the chosen energy range (0-10 eV).
0.02 eV is very small so no surprise that the first peak is so intense and not very much broadened, and also for the second peak the broadening is still quite small.
The results you show from the literature have certainly used a large broadening.
Maybe you have tried already, but if not you may try to "play" with this parameter to see whether you get a spectrum that looks like the experiment.

Cheers,
m

[andrea marini]

For metals, an accepted routine is to split the dielectric function into the intraband contribution, which is cast in the form known from the Drude free electron theory, and the interband contribution [J. Phys. Condens. Matter. 19, 196105 (2007)]. Does Yambo indeed calculate the interband contribution only or altogether (both interband and intraband)?

If you do not include the Drude term Yambo calculates interband only.

If only the interband contribution is calculated, the dielectric function should not diverge in the long wavelength limit. In fact, only another part from Drude free electron lead to diverge for ideal metal. Am I right? If yes, the BSE equation in principle should work, no matter that the system has excitonic effects or not (I mean in principle, we should not forbid/disallow this kind of calculations in the code. ). Am I right? Another question: do you expect some difference on the calculated spectra on q--->0 (yambo -b -o b -y h and change 'xc' to 'x' in yambo.in) and q=0 (yambo -o c)? If yes, what's the physics behind?

You should see NO DIFFERENCE between the two calculation IF AND ONLY IF you used the same parameters: broadening, Local field vectors, ... From all our tests the two calculations yielded the same result.

Regarding BSE I keep my point. Excitonic effects in metals (and Al is one of the king of all the metals) are meaningless if the density of electrons at the Fermi is non zero.

Now let's forget about the BSE instead using RPA. I have done a test calculation on the optical spectra of Aluminum , which is well-established both from experiment and theory [Phys. Rev. B 3, 1898 (1971) and Phys. Rev. Lett. 25, 156 (1970)]. But unfortunately I didn't obtain a nice spectrum, that is, the first peak is rather strong than the previous calculations and experiments.

I would like to add to myrta's remarks that my experience with Al is terrible. You must use a huge number of k-points to converge the absorption, unless you do not use some kind of interpolation that, at the moment, is not coded in Yambo.
My fear is the 18x18x18 is not enough and the deviations you see in your spectra is still due to the k-point sampling. Did you try to increase the size of the k-point sampling ?

Andrea

[Yunfeng]

Thank you!

You should see NO DIFFERENCE between the two calculation IF AND ONLY IF you used the same parameters: broadening, Local field vectors, ... From all our tests the two calculations yielded the same result.

Yes. it seems there is no difference from my limited experience too.

Regarding BSE I keep my point. Excitonic effects in metals (and Al is one of the king of all the metals) are meaningless if the density of electrons at the Fermi is non zero.

It is empirically right. The fact is that the updated version using (yambo -b -o b -y h and change 'xc' to 'x' in yambo.in) doesn't work too. My feeling is that some metal like graphite should have some excitonic effects, will you agree?

I would like to add to myrta's remarks that my experience with Al is terrible. You must use a huge number of k-points to converge the absorption, unless you do not use some kind of interpolation that, at the moment, is not coded in Yambo.
My fear is the 18x18x18 is not enough and the deviations you see in your spectra is still due to the k-point sampling. Did you try to increase the size of the k-point sampling ?

I also intended to believe that the width of Lorentzian broadening ~ 0.8 eV is already enough. Then the matter should be the k-point sampling, but unfortunately, I didn't succeed in larger k-point sampling. It crashed at some point in a 4-cpu AMD machine with 4 Gbye memory, will you expect this crash?

Now I'm trying to use a conventional cell with 4 atoms but still 18x18x18 Kpoint sampling, to somehow conquer the problem in different way . Unfortunately the scf calculation is idling for an overnight. Well, this is not a Yambo problem. But maybe you have already the answer! I attached the scf input below.

Al.scf.in

&control
calculation='scf'
restart_mode='from_scratch',
prefix='al'
tprnfor = .true.
tstress = .true.
pseudo_dir = '/home/liang/PP/' ,
outdir = '/localscr/liang/tmp/Al/'
/
&system
ibrav= 0, celldm(1) = 1.0, nat= 4, ntyp= 1,
ecutwfc =30.0,
occupations='smearing', smearing='marzari-vanderbilt', degauss=0.05
/
&electrons
diagonalization='david'
mixing_mode = 'plain'
mixing_beta = 0.7
conv_thr = 1.0d-8
/
ATOMIC_SPECIES
Al 26.98 Al.pbe-rrkj.UPF

CELL_PARAMETERS
7.620000000 0.000000000 0.000000000
0.000000000 7.620000000 0.000000000
0.000000000 0.000000000 7.620000000

ATOMIC_POSITIONS { crystal }
Al 0.00 0.00 0.00
Al 0.50 0.00 0.50
Al 0.00 0.50 0.50
Al 0.50 0.50 0.00

K_POINTS { automatic }
16 16 16 0 0 0


Sincerely, Yunfeng

[myrta gruning]

I also intended to believe that the width of Lorentzian broadening ~ 0.8 eV is already enough. Then the matter should be the k-point sampling, but unfortunately, I didn't succeed in larger k-point sampling. It crashed at some point in a 4-cpu AMD machine with 4 Gbye memory, will you expect this crash?

Hallo Yunfeng,

note that following your input you are applying the 0.8 eV broadening only around 10 eV, while at the energy you are interested to the broadening is much smaller (smaller or about 0.1 eV since it varies linearly). If you wish a uniform broadening of 0.8 eV you should specify
% DmRngeXd
0.80000 | 0.80000 | eV # [Xd] Damping range
%
Of course this does not solve the k sampling problem.

About the crash was there any message?
In general you can check how much memory is allocated by looking at the l_* file.
For example when WF are allocated you get something like:
<02s> [M 8.640 Gb] Alloc WF (8.625)
and the same for e.g.

So, yes it may be that 4 Gb are not enough (were you using 4 Gb for each processors or the processors were sharing 4 Gb?).

Cheers,
m

[Yunfeng]

Dear Myrta,

note that following your input you are applying the 0.8 eV broadening only around 10 eV, while at the energy you are interested to the broadening is much smaller (smaller or about 0.1 eV since it varies linearly). If you wish a uniform broadening of 0.8 eV you should specify
% DmRngeXd
0.80000 | 0.80000 | eV # [Xd] Damping range
%
Of course this does not solve the k sampling problem.

Thank you very much! This is very useful. I've played with different broadening, as follows.

Broadening.jpg

It looks better:) An annoying factor is that the peak at ~2.5 eV is very apparent, when plotting the optical conductivity. BTW: a non-uniform broadening indicates: in experiments, the higher energy, the lower resolution. Am I right?

About the crash was there any message?
In general you can check how much memory is allocated by looking at the l_* file.
For example when WF are allocated you get something like:
<02s> [M 8.640 Gb] Alloc WF (8.625)
and the same for e.g.

So, yes it may be that 4 Gb are not enough (were you using 4 Gb for each processors or the processors were sharing 4 Gb?).

The message is indeed related to the memory, but it seems not using all of the memory (it is a node with 4 CPU and sharing 4 Gb memory). The last few sentences in log files are:


" <11m-46s> [M 0.504 Gb] Free WF (0.572)


<11m-47s> [M 0.622 Gb] Alloc OptOsc (0.118)
[ERROR] STOP signal received while in :[04] Optics
[ERROR]Mem All. failed. Element WF require 1.86002 [Gb]"

Sincerely, Yunfeng

[Yunfeng]

Dear Andrea,

I would like to add to myrta's remarks that my experience with Al is terrible. You must use a huge number of k-points to converge the absorption, unless you do not use some kind of interpolation that, at the moment, is not coded in Yambo.
My fear is the 18x18x18 is not enough and the deviations you see in your spectra is still due to the k-point sampling. Did you try to increase the size of the k-point sampling ?

I have finished a calculation with conventional cell (4 atoms), in a single AMD node, the largest kpoint sampling is 16x16x16. The calculated spectra is different from the one with primitive cell (1 atom), with kpoint sampling 18x18x18. I attached the plot here.

kpoints.jpg

It is already very close to experiments up to 2.4 eV, including the relative intensity. Have you noticed the additional peak around 2.5 eV in your caculation?

PS1: for the SCF calculation on the conventional FCC cell of Al, it turns out that ecutwfc =30.0 is too large. Change it to 20-25 eV, the pw works!!

Sincerely, Yunfeng

[haseebphysics1]

Dear Myrta,

That means that the broadening varies linearly from 0.02 to 0.8 eV in the chosen energy range (0-10 eV).

Another comment you posted:

note that following your input you are applying the 0.8 eV broadening only around 10 eV, while at the energy you are interested to the broadening is much smaller (smaller or about 0.1 eV since it varies linearly). If you wish a uniform broadening of 0.8 eV you should specify

Code: Select all

% DmRngeXd
0.80000 | 0.80000 | eV # [Xd] Damping range
%

Question: I'm still unsure about how damping or broadening is applied in Yambo? e.g.
If I plot the spectrum in 0-6 eV range and I have three or more peaks in the spectrum and also apply nonuniform broadening like

Code: Select all

% DmRngeXs
0.20000 | 0.50000 | eV # [Xs] Damping range
%

How the broadening will apply to the whole spectrum? 0.5 broadening will apply close to 6eV only and 0.2 eV will apply close to 0 eV peaks? This is very confusing to me! Kindly explain in detail.

Regards,
Haseeb Ahmad,
LUMS, Pakistan.

[Daniele Varsano]

Dear Haseeb,

How the broadening will apply to the whole spectrum? 0.5 broadening will apply close to 6eV only and 0.2 eV will apply close to 0 eV peaks? This is very confusing to me! Kindly explain in detail.

Yes, as you said, it varies linearly from the first value (0.2) to the last value (0.5) in the range you have chosen. This is independent of how many peals you have in the spectrum.

Best,
Daniele

[haseebphysics1]

Dear Daniele,

If I just change the DmRngeXs value and rerun the calculation (BSE spectra) without specifying the -J option, will it start again? I mean BS kernel will again be recalculated?

I have done this by above-mentioned procedure, and now my CPU is again loaded!



Regards,
Haseeb Ahmad,
LUMS, Pakistan