metallic bands at dirac point

[a.ugolotti]

Dear Yamboers,

I am reading the transition dipole matrix elements (within IP-RPA approximantion) from a python script using netCDF and I am trying to assing the proper element to the right eigenstate. In the case of a dirac point, examining the list of Kohn-Sham eigenvalues per k-point (20, in my case) in r_optical file, I get 4 filled bands, 16 empty ones, where in K the "HOMO" is exactly at Fermi level. However, during the first steps of the calcuation of optical spectrum, the same file reports that there are 2 metallic bands, where the fully filled/empty bands are 1-3 and 6-20, respectively. Correspondingly, in every dipole fragment are stored 5 valence states per 17 conduction ones. Moreover, inspecting the values which are stored inside, the values of the dipole moment are significantly different from 0 between bands 5-1 for several k-points other than K, which is not what is was expecting. I am wondering how yambo assings an eigenstate to valence/conduction in this state. Comparing with other metallic systems, this behaviour is different from splitting a band in valence and conducion, because it seems here that each of the two degenerate dirac points are replicated in the opposite band. The system is silicene in its 1x1 cell, with an unshifted 48x48x1 k-points mesh.

Any help will be appreaciated, thank you.

Bests,

[Daniele Varsano]

Dear Aldo,
it is not easy to follow what you are asking and writing, maybe if you attach the report file it can help to understand.
Best,
Daniele

[a.ugolotti]

Yes, sure. Here it is the Yambo r_optics file, containing the list of k-points and the band infos:
https://ufile.io/0qjwmx5u

in particular :

[X]States summary : Full Metallic Empty
0001-0003 0004-0005 0006-0020
[X]N of el / N of met el : 8.000000 2.000004
[X]Average metallic occ. : 0.500001

The bands are reported in the pic attached here https://ibb.co/QN8SyvN: the only points which can be seen as metallic are the two forming the "almost" dirac point in K.

I can guess from such data that the degenerate eigenvalues at the dirac point are somwhat replicated, i.e. forming new (non complete along k space) bands. In fact, just inspecting the dipole matrix elements, which are collected in the text file attached here https://uploadfiles.io/yd4w8afk, there are 5 valence bands and 17 conduction ones. However i am expecting to find dipoles significantly different from zero for the transition v=5 --> c=1 only on K (i.e. k-point 217), instead there are several non-zero dipole for such transition at other k-points. In addition, the magnitude of the dipole (actually, its squared modulus) of ~10^(+11) suggest me that the transition is taking place between to state almost degenerate in energy as the two found in K. Well, such magnitude can be found not just for the 5-->1 transition, but also for the 4-->2 one, for example.
Hence there is something I am not understanding in how Yambo assigns eigenvalues to valcence/conduction band in this case.
As a complete reference, after reading the pair (k-point,eigenvalue) from r_optics file, I wrote a script which defines a matrix for the valence band an one for the conduction one. In my case the splitting is done by simply checking if eigenvalue>0 (the energies are already referred to Ef) and checking the number of metallic bands.

[Daniele Varsano]

Dear Aldo,
note you can upload a file directly in the forum clicking on "Upload attachment" button. In order to make it works you need to rename the file as .txt or other allowed suffix (.zip etc.).
Being it a metal Yambo assigns fractional occupation using a Fermi-Dirac distribution with a given temperature. By default it is 300K

Code: Select all

 [X]Electronic Temp. [ev K]: 0.2585E-1  300.0

So as stated in the report bands 4-5 are partially occupied with a fractional occupation.

In your dipole table, the valence 4 and conduction 1 are the same bands as well as the valence 5 and the conduction 2.
These two bands at K point are degenerate.

valence index. conduction index
5 ---------- 2
4 ---------- 1

As you can see <5|r|1>=<4|r|2>
<4|r|1>=<5|r|2>

These dipole elements are then calculated twice, but then being half occupied are reweighted with the occupation number (here=1/2).
The electronic temperature can be also controlled by input by the variable,

Code: Select all

 ElecTemp=

Actually, in your case, you have a very small gap at K of about 0.01 meV.
You can try to run the code by setting:

Code: Select all

ElecTemp= 0 eV

and see if the system is then "seen" as a semiconductor with nearly zero gap, in this case, you will have integer occupation numbers: in this case, these will be calculated just once with weight equal 1.

Hope this answers to your question.

Best,
Daniele

[a.ugolotti]

Dear Daniele,
thank you for the clear explanation. If I got this correctly, the transition-dipole matrix elements should then be moltiplied by the electronic occupation of the final and initial state. Plus, there should be some check over the negative energy difference, namely v=5->c=1 is the symmetric (and therefore the squared modulus is the same) of 4->2 but should not be allowed, since c=1 is the weighted replica of v=4; is that correct?
As for the upload of an attachment, I will keep in mind for the next occasion.

[Daniele Varsano]

Dear Aldo,

If I got this correctly, the transition-dipole matrix elements should then be moltiplied by the electronic occupation of the final and initial state.

Yes, In the response function, all the transition are then summed up with the corresponding occupation number.

Plus, there should be some check over the negative energy difference, namely v=5->c=1 is the symmetric (and therefore the squared modulus is the same) of 4->2 but should not be allowed, since c=1 is the weighted replica of v=4; is that correct?

It is allowed as 2 is half occupied and 4 is half empty. Then there is an occupation factor 2f(1-f) taken into account.

Best,
Daniele

[a.ugolotti]

Ok, I understand. Thank you again.

Bests,

Aldo