Semi metallic behavior in semiconductor superlattice;

[Zahra Taghipour]

Dear Developers and Users,

I have a conceptual question:
I am working on a semiconductor superlattice that has an experimental Gamma-to-Gamma transition of 280 meV.
On the other hand, I am trying to simulate this structure within DFT using QE to study the excitons (to be corrected with GW in Yambo).

What I see is a semi-metallic behavior: highest occupied is at Gamma, and lowest unoccupied is at the border of BZ (L point: 0.5, 0.5 0) and lower than highest occupied at Gamma! This behavior is seen for a couple of different PP’s.

GW corrects Gamma-to-Gamma transition pretty well, which is very close to the experiment; But, the semimetal behavior is still present.
So, here is my question:

Lets’ say the Temperature is low. Experimentally, one excites the electron at Gamma (correct?), therefore, how one sees the semi-metal effect in the experiment at other k-points (Where does the fact that there is a k-point in the border that has lower unoccupied state than the highest Gamma show itself in the experiment)?

I have tried relaxing my structure, applying COHSEX+GW, so far. Unfortunately, Yambo does not accept a manual k-grid and I could not find a way to have gamma point, and avoid L point, simultaneously.

I realize that my question is probably above the scope of this forum, but I hope to find the answer to my confusion from the experts in the forum.
Any comment is really appreciated.

Yours

Zahra
Ph.D. student, Center for High Technology Materials, Univ. of New Mexico, USA

[Daniele Varsano]

Dear Zahara,

On the other hand, I am trying to simulate this structure within DFT using QE to study the excitons (to be corrected with GW in Yambo).

Beware that GW does not give you excitonic peak but quasiparticle energy level, in order to look at exciton you need to solve the Bethe Salpeter equation.

GW corrects Gamma-to-Gamma transition pretty well, which is very close to the experiment;

Again, if GW gap it is similar to the optical gap it means that there are very small excitonic effects.

But, the semimetal behavior is still present.

Not that strange, GW is a perturbation theory, so hardly it can change the character you found at DFT level.

Experimentally, one excites the electron at Gamma (correct?), therefore, how one sees the semi-metal effect in the experiment at other k-points (Where does the fact that there is a k-point in the border that has lower unoccupied state than the highest Gamma show itself in the experiment)?

Well, in my opinion it is important to understand where it is placed the Fermi energy. If I understood correctly what you described at 0K in your situation you could have the top of valence bands at gamma unoccupied. It is not very clear what do you mean saying that the electrons are excited at gamma.

I have tried relaxing my structure, applying COHSEX+GW, so far.

What do you mean by relaxing? There are not force implemented at this level of theory in Yambo (and in other codes neither as far as I know).

Unfortunately, Yambo does not accept a manual k-grid and I could not find a way to have gamma point, and avoid L point, simultaneously.

Well, the important think is that the K grid is regular. You can generate a regular K point grid containing a specific K point (maintaining the q grid of your original sampling) to be used in quantum espresso by using the ypp utility (ypp -k k).

Best,
Daniele

[Zahra Taghipour]

Dear Daniele,

Thank you for your response.
Sorry, I think I did not explain my problem very well.

At this point, I want to do the gap correction. My structure is a semiconductor superlattice with an experimental gap of 0.250 eV.
However, QE gives a semimetallic behavior at (0.5,0.5,0) in a way that its CB and VB are lower than Gamma point's gap! I have relaxed my structure in QE.
I have used GW correction in Yambo on different k-points, and the gap at gamma after this correction is similar to the experiment. However, CB and VB at L-point is still below the gamma, which is not surprising since GW does not change the DFT result that way!

you could have the top of valence bands at gamma unoccupied

I just fail to understand what would happen experimentally if in fact the L-point gap is lower than Gamma-gap.
As far as I know, in the experiment, the optical gap is due to carrier transition at gamma point. So, carriers tend to relax back to gamma point in a very short time. So, the experimental gap measurements are considered to be at gamma!

I have tried applying gw correction on COHSEX QP results (instead of DFT), using <XfnQPdb= "E < ./SAVE/ndb.QP">, however, I am not sure if this is the correct way for it?
I have read in an old post that applying gw on Cohsex is not possible. is it still so?

You can generate a regular K point grid containing a specific K point

I have tried to eliminate (0.5,0.5,0) from my k-grid in order to eliminate the Semi-metalic behavior and check the results, but Yambo gives this error for non-uniformity of k-grid! So, I do not know how to generate a uniform k-grid Not containing a specific point!

Thank you so much,
Best,
Zahra

[Daniele Varsano]

Dear Zahra,

As far as I know, in the experiment, the optical gap is due to carrier transition at gamma point. So, carriers tend to relax back to gamma point in a very short time. So, the experimental gap measurements are considered to be at gamma!

Again, I do not get this point. Why transition from gamma only? If you look at independent particle level, you will have have all the possible transitions from occupied to unoccupied states with the condition K=K'=0 (vertical transitions). With gamma you mean zero transferred moment?

I have tried applying gw correction on COHSEX QP results (instead of DFT), using <XfnQPdb= "E < ./SAVE/ndb.QP">, however, I am not sure if this is the correct way for it?

Well, I would need to look at the input in order to say if it is correct or not. What I can tell you is that in this way you are using QP energies (I do not know if GW or cohsex) in the polarization matrix, but I do not know if you are now using it for optics (RPA) or to calculate the screening for a GW calculation.

I have read in an old post that applying gw on Cohsex is not possible. is it still so?

Self consistency is still experimental so not yet released under the GPL distribution.

I have tried to eliminate (0.5,0.5,0) from my k-grid in order to eliminate the Semi-metalic behavior and check the results, but Yambo gives this error for non-uniformity of k-grid! So, I do not know how to generate a uniform k-grid Not containing a specific point!

Yes you cannot simply eliminate a point from the grid. What you can do is to try to generate shifted grid with quantum espresso.

Best,
Daniele

[Zahra Taghipour]

Dear Daniel,

In one of your previous posts, you had suggested that I'd use shifted k-grid. Recently, I used a shifted grid in my ground state calculation: 661111!
However, there is this error "[ERROR] STOP signal received while in :[03] Transferred momenta grid ... [ERROR]Error in Q-grid search [qindx_X]" I get when I try to start the GW calculation. I read the other posts saying that it is not possible to use the shifted k-grid in yambo!
I just wanted to make sure if this is still the case in the newer version of yambo, or is there any suggestion that might help me solve this issue? I'd appreciate it.

Thank you,
Zahra Taghipour,
Ph.D. student, UNM, USA

[Daniele Varsano]

Dear Zahra,
of course you can use shifted grids. What you can't use is non-uniform grid, which is a different story.
I do not know that can be wrong with the setup, have you set the keyword:

Code: Select all

force_symmorphic=.true. 

in the system namelist of quantum espresso run. If you did not try do add it and repeat the calcualtions.
If it fails again you can post your scf/nscf qe inputs as in order to understnad what is going we need to reproduce the error.

Best,
Daniele

[Zahra Taghipour]

Dear Daniele,

I had forgotten to add the force_symmorphic line in the first place. Although I did not get the mentioned errors anymore, still it does not allow me to follow my calculation due to "non-uniform k-grids". I believe it should not be the case since I only shifted the k-points (automatic).
I have attached the inputs from the QE and the r_setup I get in Yambo, and I would really appreciate if you could kindly help me resolve this issue.

Thank you,
Best,
Zahra Taghipour,
PhD Student, UNM, USA

[Davide Sangalli]

Dear Zahra Taghipour,
I would suggest not to shift the k-griz along-z, i.e. to use 6 6 1 1 1 0

Would it work like that ?

Best,
D.

[Davide Sangalli]

Dear Zahra Taghipour,
I did some check on the kpoints sampling.

I think the problem is that pwscf is not just doing a simple shift.
If you check, you will see that there is kpts dispersion also along the z grid,
despite the fact that you asked for one kpt only along z.

I tried to plot the k-points grid, but it does not seem a regular grid to me.
Only if I try a 6x6x6 grid or if I center the grid in gamma it is then regular.

D.

[Zahra Taghipour]

Dear Davide,

Thank you for your response.
I did as you suggested and it worked for 661110 kpnt sampling!
I really appreciate your help.

With Regards,
Zahra