## q-polarization in nano-wires

Deals with issues related to computation of optical spectra, in RPA (-o c) or by solving the Bethe-Salpeter equation (-o b). Includes local field effects, excitons, etc.
DavidPolito93
Posts: 15
Joined: Sat Jun 06, 2020 10:43 am

### q-polarization in nano-wires

Dear Developers,

I am trying to do some gw computations in 1D systems, in particular nano-wires. I am using a cylindrical cut-off with no RIM:

CUTGeo= "cylinder Z" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere/ws X/Y/Z/XY..
%

In the tutorials, when dealing with bulk h-BN, if we want to compute the gw band-structure we set:

%LongDrXp
1.00000 | 1.00000 | 1.00000

so that the electric field is directed in a non-generic direction.
Now, I have seen in the wiki that:

"Usage: Pay attention how the system is oriented when treating non 3D systems and choose a direction in the plane/axis where your system lies"

So I assume that, if my system is distributed along the z-axis (periodic direction), I should set:

%LongDrXp
0.00000 | 0.00000 | 1.00000

However, in the 2D h-BN tutorial you show that depending on the polarization (along the periodic direction or along the non-periodic direction) we get shifted absorption spectra. So my question is:

The LongDrXp direction should have also an effect on the G0W0 band structure, am I wrong?
So, which one should be used for computing quasiparticle band-structures?

Best,

Davide Romanin
-----------------------------------------------------
PhD student in Physics XXXIII cycle
Representative of the PhD students in Physics
Applied Science and Technology department (DiSAT)
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino ITALY
------------------------------------------------------

Daniele Varsano
Posts: 2605
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: q-polarization in nano-wires

Dear Davide,
I am using a cylindrical cut-off with no RIM:
This should be ok, but in case you have an orthorhombic cell, I strongly suggest you use the wigner-seitz cutoff as it is more stable and do not require regularization.

Code: Select all

``````CUTGeo= "ws z"
CUTwsGvec= 0.700000``````

The LongDrXp direction should have also an effect on the G0W0 band structure, am I wrong?
The choice affects the calculation of the dipoles so it is very relevant for the absorption, while in the GW calculation should not be so relevant provided that you include the z-direction as in your case should be the direction with higher absorption and the more relevant for the screening so I would use this for the GW. For the absorption, it depends on the direction you want to look at. The z will be the more relevant, the other directions could be of interest if you are interested in depolarization effects. Se e.g. Marinopoulos et al Phys. Rev. Lett. 91, 046402.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

DavidPolito93
Posts: 15
Joined: Sat Jun 06, 2020 10:43 am

### Re: q-polarization in nano-wires

Dear Daniele,

Yes, indeed I saw that the effects of depolarization were discussed in the various tutorials and I was wondering if they had some effects also on the quasiparticle band structure.

For what concerns the cut-off, I am using a tetragonal unit cell. So the ws cutoff should avoid the cut-off radius convergence of the cylinder, am I right?

Davide
-----------------------------------------------------
PhD student in Physics XXXIII cycle
Representative of the PhD students in Physics
Applied Science and Technology department (DiSAT)
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino ITALY
------------------------------------------------------

Daniele Varsano
Posts: 2605
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: q-polarization in nano-wires

Dear Davide,
For what concerns the cut-off, I am using a tetragonal unit cell. So the ws cutoff should avoid the cut-off radius convergence of the cylinder, am I right?
Yes, in the ws cutoff you do not need to specify any geometrical parameter as it is automatically set to the WS of your cell. You just need to have a cell with is sufficently large (e.g. a bit larger than twice the dimension of your system, as you need to consider some spillout of your density) and a convergency check of the k points samplings. Note that these two conditions applies also for the cylinder. Then you have a cutoff on the number of gvectors to be modified, usually, a value 0.7-1.5 is ok.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

DavidPolito93
Posts: 15
Joined: Sat Jun 06, 2020 10:43 am

### Re: q-polarization in nano-wires

Dear Daniele,

Just a rapid question concerning the ws cut-off:

If I set CUTGeo= "ws z" it means that it will cut the Coulomb interaction along x and y right?

Davide
-----------------------------------------------------
PhD student in Physics XXXIII cycle
Representative of the PhD students in Physics
Applied Science and Technology department (DiSAT)
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino ITALY
------------------------------------------------------

Daniele Varsano
Posts: 2605
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: q-polarization in nano-wires

Dear Davide,
you are right I did not specify this point. Actually you need to indicate a direction in the input just for internal consistency in the code and activate the cutoff, but it does not take any real effect. The ws cutoff truncates the interaction in the WS super-cell, ie Lx/2, Ly/2, nkz*Lz/2, in the case of a wire along z. So it needs a convergence with respect to the sampling. Note that also in the case of a cylinder the interaction along z is cut beyond a certain distance in order to avoid divergences.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/