The physical of amplitude

[Guo_BIT]

Dear developers:
By adjusting parameter BLongDir, we performed BSE calculations in different directions, and find anisotropy exists in our system.
My supervisor suggests that the change of oscillator strength is related to Acv in these expressions:

and

However, I found that the o-amplitude files from different calculations are all same.

Furthermore, in other topics, professor Varsano mentioned that Acv are the eigenvectors of the BSE, and a practical exciton is a composition (superposition) of multiple states weighted by Acv.
So, my personal understanding is that Acv acts as a probabilistic parameter. A higher the value it in o-amplitude files, the greater the possibility of excitons existing at this energy. Therefore, this parameter is independent of the change of oscillator strength and direction.

Could you please confirm whether my interpretation is correct?

Best,
Jingda Guo

[Daniele Varsano]

Dear Jingda,

the amplitude file is defined as: amp(omega)=\sum Acv *1/(omega-(Ec-Ev). It is independent of the polarization and provides information on the
energy range of the transitions participating in an exciton. The higher the amplitude, the more are the transitions participating in that energy range.

If you want to look at the change in the oscillator strength, it is possible to look at the product |Acv*<v|d|c>|^2
You need to add the keyword dipoles in the ypp input file, e.g.

Code: Select all

excitons                         # [R] Excitonic properties
amplitude                        # [R] Amplitude
dipoles
States= "1 - 1"                  # Index of the BS state(s)
BSQindex= 1                      # Q-Index of the BS state(s)
Degen_Step= 0.010000       eV    # Maximum energy separation of two degenerate states

the result is stored in the *weight file, and note that the weight are not normalized to one anymore.

Best,
Daniele

[Guo_BIT]

Dear Varsano,
Thank you for your patient explanation.
We made changes to our input file according to your suggestion as follow:

Code: Select all

excitons                         # [R] Excitonic properties
amplitude                        # [R] Amplitude
dipoles
States= "1 - 6"                  # Index of the BS state(s)
BSQindex= 1                      # Q-Index of the BS state(s)
Degen_Step= 0.0000       eV    # Maximum energy separation of two degenerate states

The output, named as o*exc_qpt1_weights_and_dipoles_at_1, however, is not consistent with our expectations.

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# Electron-Hole pairs that contribute to Excitonic State 1 for iq=1 more than  5.000000%
#                       K-point [iku]                         Weight
# :  -0.500000000         0.00000000         0.00000000         1.00000000   
#    
#
#    Band_V             Band_C             Kv-q ibz           Symm_kv            Kc q ibz           Symm_kc            Weight             Energy [eV]
#
         36                 37                289                1                  289                1                  0.999976           0.073148
# 
# 04/07/2024 at 10:11 ypp @ j2 [start]
# 04/07/2024 at 10:11          [end]
#  
# Timing   [Min/Max/Average]: 03s/03s/03s
#
# .-Input file  ypp_AMPL.in
# | excitons                         # [R] Excitonic properties
# | dipoles                          # [R] Dipole properties
# | amplitude                        # [R] Amplitude
# | DIP_kind= "^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^
@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@" # Kind of DIPOLES use (IP, EXCITONIC, MASK)# | cooOut= "rlu"                    # Points coordinates (out) cc/rlu/iku/alat
# | % DIP_E_range
# | -1.000000 |-1.000000 |         eV    # E/h pairs energy window
# | %
# | % DIP_direction
# |  0.707107 | 0.707107 | 0.000000 |        # Field direction versor
# | %
# | States= "1 - 6"                  # Index of the BS state(s)
# | BSQindex= 1                      # Q-Index of the BS state(s)
# | Degen_Step= 0.000000       eV    # Maximum energy separation of two degenerate states

This result is basically the same as when I didn't add the parameter 'dipoles' in my input file, and parameter DIP_kind looks odd
We are using version 5.2. Is there any problem with my input file?

[Daniele Varsano]

Dear Jingda,
indeed, your result seems weird.
I suggest you to generate the input file step by step:

No dipole weight:

Code: Select all

>ypp -e a -b 1 -F ypp_nodipoles.in

Weighting with dipoles:

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>ypp -e a -b 1 -d exc -F ypp_withdipoles.in

and compare the results of the two calculations using the generated ypp.in files. You will need to set Degen_Step if you want analyze a single excitation without taking into account the degeneracy.

Best,
Daniele