Analysis of dark exciton

[Dhanjit]

Dear Daniele,
I must have missed the granting access part to the drive link. Below is the link to the folder containing the input files and report files of the system.
https://drive.google.com/drive/folders/ ... sp=sharing

[Daniele Varsano]

Dear Dhanjit Talukdar,

as you can see from the report, the calculations seem to be correct. You have degenerate spin-up sin-down quasiparticle energy.
The problem is in the interpolation results and seems that is just a matter of unit conversion, spin-up are in eV while spin down are in Hartree.
Thanks for reporting, I will check if the mismatch is also present in the latest version of Yambo (you are using a quite old release) and fix it if needed.
At the moment, you can easily get the correct plot by multiplying the spin down energies by the unit conversion factor (27.2114).

Best,
Daniele

[Dhanjit]

Dear Daniele,
I have corrected the conversion error as suggested.
Now, if I use the ndb.QP file in solving the BSE, it should effect the optical transitions too, right?

[Daniele Varsano]

Dear Dhanjit Talukdar,
you can safely use the ndb.QP as internally is all stored in Hartree units. Conversion to eV is done only in the output files.

Best,
Daniele

[Dhanjit]

Dear Daniele,
I have tried the ndb.QP file for calculating the excitonic properties and got a bit confused with the "exc_qpt1_weights" output file.

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#    Band_V             Band_C             Kv-q ibz           Symm_kv            Kc ibz             Symm_kc            Spin
#    
   150.000000      154.000000      36.0000000      2.00000000      36.0000000      2.00000000      1.00000000     0.112382963      1.82091212   
   150.000000      154.000000      36.0000000      2.00000000      36.0000000      2.00000000     -1.00000000     0.112306878      1.82091618   
   150.000000      154.000000      36.0000000      1.00000000      36.0000000      1.00000000      1.00000000     0.112091124      1.82091212   
   150.000000      154.000000      36.0000000      1.00000000      36.0000000      1.00000000     -1.00000000     0.111989975      1.82091618   
   150.000000      154.000000      29.0000000      2.00000000      29.0000000      2.00000000      1.00000000     0.105052233      1.82429767   
   150.000000      154.000000      29.0000000      2.00000000      29.0000000      2.00000000     -1.00000000     0.104975253      1.82430100   
   150.000000      154.000000      29.0000000      1.00000000      29.0000000      1.00000000      1.00000000     0.104809165      1.82429767   
   150.000000      154.000000      29.0000000      1.00000000      29.0000000      1.00000000     -1.00000000     0.104705133      1.82430100   
   150.000000      154.000000      22.0000000      2.00000000      22.0000000      2.00000000      1.00000000     0.575463995E-1   1.88473892   
   150.000000      154.000000      22.0000000      2.00000000      22.0000000      2.00000000     -1.00000000     0.575051084E-1   1.88474178   
   150.000000      154.000000      22.0000000      1.00000000      22.0000000      1.00000000      1.00000000     0.574879423E-1   1.88473892   
   150.000000      154.000000      22.0000000      1.00000000      22.0000000      1.00000000     -1.00000000     0.574273504E-1   1.88474178   

Can you help me out with the last three columns signify exactly?

[Daniele Varsano]

Dear Dhanjit,

the weight file provide you the bands/kpoints/spin participating to the exciton and it is organized as follows:

Columns(1:2) Valence and Conduction bands
Columns(3:4) K point of the valence band given as K points in the IBZ and its symmetry operation (symmetry operation index can be seen in the report file)
Columns(5:6) K points of the conduction band
Column(7) Spin index (1=spin_up, -1=spin_dn)
Column(8) weight of the transition defined as |A_cv|^2 where A_cv is the eigenstate of the BSE
Column(9) Energy difference Ec-Ev (note here QP correction are not taken into account).

Also note that Sum_cv |Acv|^2 for a single exciton is 1.
If you are considering degenerate excitons o excitons nearby in energy it is equal to the number of excitons accounted.

If you want to analyze a single exciton yuou need to set in the ypp input file the energy degeneration threshold to zero (Degen_Step=0. eV). The default value is 0.01 eV.

Best,

Daniele

[Dhanjit]

Dear Daniele,
Thank you for your swift reply, and kindly accept my apologies for replying such late.
The information below is a weight file for a dark exciton, and the calculation is done with spin polarisation.

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Band_V	Band_C	K-VB	Sym-VB	K-CB	Sym-CB	Spin index	weight	energy
								
151	154	36	2	36	2	-1	0.0857239291	1.77928221
151	154	36	2	36	2	1	0.0856413096	1.77927935
151	154	36	1	36	1	-1	0.0856242999	1.77928221
151	154	36	1	36	1	1	0.0855332911	1.77927935
151	154	29	2	29	2	-1	0.0666700453	1.80336022
151	154	29	1	29	1	-1	0.0666668415	1.80336022
151	154	29	2	29	2	1	0.0665938556	1.80335748
151	154	29	1	29	1	1	0.0665891618	1.80335748
150	153	43	1	43	1	-1	0.0626232922	1.27444911
150	153	43	1	43	1	1	0.0625829697	1.27441978
151	154	43	1	43	1	-1	0.0515657812	1.80314541
151	154	43	1	43	1	1	0.0515052713	1.80314231

Now, is it possible to find out whether the exciton is momentum forbidden or spin forbidden? As there is no change of k point in CB or VB. Is it a spin forbidden exciton as the spin index in 5,6,7,8 row of the above table follow a different pattern than the rest.

[Daniele Varsano]

Dear Dhanjit,

This excitation is not momentum forbidden as you are calculating an excitation with q=0 (i.e. same kv and kc). Finite momentum excitations are calculated when setting BSEQptR different from 1 in the input file.
I would say it is neither spin forbidden, in a collinear spin polarized calculation you can distinguish singlet and triplet excitations, and triplet excitation can be calculated by removing the Kx term from the excitonic Hamiltonian (see e.g. Rohlfing and Louie PRB 62 2000 Eq. 25 and discussion in the text).

I would say that this is a dipole forbidden excitation.

Best,

Daniele