Analysis of dark exciton

[Dhanjit]

Dear all,
I am trying to study a degenrated interlayer dark exciton in a 2D/2D vdW heterostructure (type II band gap). One component of the doubly degenerate exciton is bright and confined to a single layer, while the other component is dark and interlayer (which I got to know after calculating the average electron/hole density). From the o-2D_BSE.exc_weights_at_7 file I got to know the CB/VB and the K-point where the transition has occured.

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#    Band_V             Band_C             Kv-q ibz           Symm_kv            Kc ibz             Symm_kc            Weight             Energy
#    
   152.000000      153.000000      1.00000000      1.00000000      1.00000000      1.00000000     0.890895352E-1   1.09779966   
   152.000000      153.000000      8.00000000      1.00000000      8.00000000      1.00000000     0.835946798E-1   1.09977186   
   152.000000      153.000000      8.00000000      2.00000000      8.00000000      2.00000000     0.835803971E-1   1.09977186   
   152.000000      153.000000      15.0000000      1.00000000      15.0000000      1.00000000     0.688678995E-1   1.10560560   
   152.000000      153.000000      15.0000000      2.00000000      15.0000000      2.00000000     0.688425601E-1   1.10560560 

In general, dark excitons are either spin forbidden or momentum forbidden. Is there any way I can further analyse this interlayer dark exciton to know whether it is spin/momentum forbidden?

[Daniele Varsano]

Dear Dhanjit,

there is something odd in your weight output.

The sum of the weights should be normalized to 1 and this is not the case here. Ypp by default merges degenerate states and in this case the normalization is the number of the degeneracy. Be sure that you set in your ypp input:

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Degen_Step = 0.0 eV

In this way, all the exciton are analysed singularly.

Coming to your question, if your calculation is not done with collinear spin (ie without spin-orbit) solving the BSE including both exchange and direct part of the kernel you are calculating singlet excitons, so they are spin allowed. Dark states in this case are dipole forbidden.

You can also calculate spin-forbidden excitons (triplet) by including only the direct term in the kernel (BSENGexx=0.0 eV). This is explained for instance in Rholfing and Louie PRB 62, 4927 (2000) (Eq.25 and text below).

In case your calculation includes spin-orbit instead singlet and triplet are not defined.

Finally, note that you calculated excitons in q=0 limit (optical limit), in order to calculate finite momentum excitons you need to indicate the desired momentum range in the BSEQptR variable (the index 1 is the q=0 limit).

Best,

Daniele

[Dhanjit]

Dear Daniele,
Thank you for you swift response. Kindly correct me if I have got your response accurately.
My calculations in QE does not include spin-orbit. Thus, to calculate the spin forbidden triplets I need to set BSENGexx= 50 Ry to 0, and then I should do the BSE solver, right?
Note: In my BSE kernel and BSE solver inputs the momentum is set as

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% BSEQptR
 1 | 1 |                             # [BSK] Transferred momenta range

.
This mean I am not calculating in optical limit q=0, right?

Lastly,
The weights didn't sum up to 1 because I posted the transitions only for the dark component. The weights I with two exciton merged is as follows:

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#    Band_V             Band_C             Kv-q ibz           Symm_kv            Kc ibz             Symm_kc            Weight             Energy
#    
   150.000000      154.000000      36.0000000      1.00000000      36.0000000      1.00000000     0.121567860      1.82096827   
   150.000000      154.000000      36.0000000      2.00000000      36.0000000      2.00000000     0.117339119      1.82096827   
   150.000000      154.000000      29.0000000      1.00000000      29.0000000      1.00000000     0.107961722      1.82435262   
   150.000000      154.000000      29.0000000      2.00000000      29.0000000      2.00000000     0.104288779      1.82435262   
   150.000000      154.000000      43.0000000      1.00000000      43.0000000      1.00000000     0.100766003      1.86904275   
   152.000000      153.000000      1.00000000      1.00000000      1.00000000      1.00000000     0.893174410E-1   1.09779966   
   152.000000      153.000000      8.00000000      1.00000000      8.00000000      1.00000000     0.838114396E-1   1.09977186   
   152.000000      153.000000      8.00000000      2.00000000      8.00000000      2.00000000     0.837872401E-1   1.09977186   
   152.000000      153.000000      15.0000000      1.00000000      15.0000000      1.00000000     0.690460429E-1   1.10560560   
   152.000000      153.000000      15.0000000      2.00000000      15.0000000      2.00000000     0.690035224E-1   1.10560560   
   150.000000      154.000000      22.0000000      1.00000000      22.0000000      1.00000000     0.579372458E-1   1.88478065   
   150.000000      154.000000      22.0000000      2.00000000      22.0000000      2.00000000     0.558769964E-1   1.88478065  

With regards,
Dhanjit

[Daniele Varsano]

Dear Dhanjit,

1: I need to set BSENGexx= 50 Ry to 0, and then I should do the BSE solver, right?

Right

2. This mean I am not calculating in optical limit q=0, right?

Yes, you are in the optical limit. iq=1 is always the q->0 limit

3. The weights didn't sum up to 1 because I posted the transitions only for the dark component.

The weight of a *single* exciton should sum up to 1. Is it possible you are weighting them with dipoles? i.e. you have the dipoles flag in your ypp input file?

Best,

Daniele

[Dhanjit]

Dear Daniele,
Kindly accept my apologies for replying such late.
I my ypp input the the DipWeight flag is commented. May be I have have missed something in the input file or else!! I am attaching the input and output files. It would be of great help if you could kindly help me out with the error. The exciton states I am interested in are 7. At first I tried calculating using

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Degen_Step= 0.010000       eV

exc_qpt1_weights_at_7.txt

The two states 7 & 8 were merged at this energy separation value. Thus I tried it with lowering the energy step again.

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Degen_Step= 0.001000       eV

exc_qpt1_weights_at_7_01.txt

At the above energy separation the weights do not sum upto 1 but when the states (7&8) are merged they sum upto 1.

[Daniele Varsano]

Dear Dhanjit,

I think it is OK, please note that by only weight > 5% are reported. If you want to check the normalization carefully you need to print also smaller weights. This can be done adding in the input file something as:
Weight_treshold= 0.010000
this will print > 1%, and you can set it to zero if you want all the weights.

Note, you need to look at the column Weight (the one before Energy). The one reported together with the k points is instead renormalized to the maximum value of the weight.

To be sure to analyze just one exciton at once, you can set:

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Degen_Step=0.0 eV

Best,
Daniele

[Dhanjit]

Dear Daniele,
I would like to add one more query regarding the spin polarized band calculation. For the current system I tried calculating spin polarized QE calculation and then GW. On DFT level the system is non magnetic and the band structure is as follows:

QE_band.png

But after, GW calculation I see some peculiar results. Both spin down and up bands after GW calulation lie at different energy level and the dispersion is vary unusual for a nonmagnetic system. The band structure without QP correction is

GW_DFT_band.png

The up bands are flat and does not overlap like it does in QE band above. Moreover when zoomed into the Y scale, it can be seen that the up bands also have the same dispersion (shape) as down bands but energy levels differs drastically. The same happens for QP corrected band as well.

GW_QP_band.png

[Daniele Varsano]

Dear Dhanjit,

sorry but from your post I cannot understand what is DFT and what GW.
The easiest way to look into it is to have a look at the yambo report file if the calculation.

Best,
Daniele

[Dhanjit]

Dear Daniele,
Apologies for the inconvenience.
The first band structure in the above post is from QE, where spin up and spin down states are overlapping. Magnetic moment is zero.

Fig1.png

The second and third figures are from yambo.
Second one (without quasi-particle correction) is done using

#GfnQPdb= "E < ./all_Bz/ndb.QP"

Fig2.png

Third one (with quasi-particle correction) is done using

GfnQPdb= "E < ./all_Bz/ndb.QP"

Fig3.png

I have also attached the r_setup file along with (uploaded to my GDrive due to large size).
https://drive.google.com/drive/folders/ ... drive_link
The spin up bands (black color) in yambo generated band structure (Fig2 and 3) do not overlap with spin down bands (red color). They look like some flat bands holding together. When I zoom into the flat bands (spin up bands-black), I notice that the up bands also have the same shape as the down one. The zoomed in picture is shown in the right side of Fig.2 & 3.

[Daniele Varsano]

Dear Dhanjit,

thanks, not it is clear!

It is important to understand if this is a problem of the calculation of just some mismatch in plotting/interpolating etc. with some unit conversion etc...
Can you post the report of the GW calculations?
If it was present in the link you provided, you should guarantee access to the drive directory.

Best,
Daniele