wave vector and frquency dependent Dielectric function using Yambo

[muhammadhasan]

Hi,

I am new in the yambo community. I have a question regarding dielectric function calculation using Yambo.
In the following equation, $S(\omega)$ is a transmission function, $\epsilon_1$ and $\epsilon_2$ are real and imaginary dielectric functions respectively. If we notice the equation carefully, we need $\epsilon (q, \omega)$ since the summation includes all the q points in the 1st BZ.

***I also uploaded the equation in the attachment****
$S(\omega) = \frac{1}{A} \sum_{q \in \text{1BZ}} \frac{4e^{-2qd} \, \text{Im}\left[\epsilon_1^{-1}(q, \omega)\right]_{00} \, \text{Im}\left[\epsilon_2^{-1}(q, \omega)\right]_{00}}{\left|1 - e^{-2qd} \left[\left(\epsilon_1^{-1}(q, \omega)\right)_{00} - 1\right] \left[\left(\epsilon_2^{-1}(q, \omega)\right)_{00} - 1\right]\right|^2}$

Normally if I do DFT using Quantum Espresso, I would get the dielectric function ($\epsilon$) over frequency ($\omega$) ranges. Are there any ways I would get dielectric function $\epsilon(\omega)$ at each q point using Yambo? If yes, would you please refer me any guidelines that I would follow?
The link of the paper related to the equation (9) (https://journals.aps.org/prapplied/abst ... .14.024080)

Thank you in advance for your time.

Best
M J Hasan
PhD Student
Mechanical Engineering
University of Maine

[Daniele Varsano]

Dear M J Hasan,
yes, you can calculate q dependent dielectric function in both RPA and BSE framework.
Using the variable QpntsRXd you indicate the first and the last q point index you want to calculate the response function in RPA.
BSEQptR, instead is the variable to be used in BSE calculation. The index "1" is the optical limit q->0, the other q indexes corresponds to the finite q of your sampling you can find in the report file, e.g. r_setup.

Best,

Daniele

[muhammadhasan]

Hi Daniele Varsano,

Thank you so so much for your reply. Basically, I need the RPA framework within Independent particle approximation. I started reading the yambo documents. However, I am confused with two things which are as follows
The input file I prepared:
optics
chi
Chimod="IP"
% QpntsRXd
1 | 19 |
%
% BndsRnXd
1 | 10 |
%
NGsBlkXd= 1 RL
% EnRngeXd
0.00000 | 10.00000 | eV
%
% DmRngeXd
0.10000 | 0.10000 | eV
%
ETStpsXd= 100
% LongDrXd
1.000000 | 0.000000 | 0.000000 |
%

Confustion1: If I choose the q points as above, Should I add the electric field direction too as LongDrXd in the input file? I am thinking that with the q points I have already defined the momentum and direction, then why we need to use LongDrXd in that case?

Confustion2: At each energy (ev), there will have some q points (say 10 q points) dependent dielectric function. So if I define the energy range from 0 to 5 ev, would it generate the 10 q points dielectric function on each enegry (ev)? Or Would I have to run the input file considering only one Energy value on each run?

I am sorry for too many questions. But your answer would clarify my confusions. Thanks again in advance.

Best
M J Hasan
Mechanical Engineering
University of Maine

[Daniele Varsano]

Dear M J Hasan,

1) why we need to use LongDrXd in that case?

Direction and momentum are defined for all the q points, except the q=0 limit (iq=1). LongDrXd is needed for this point (Long wavelenght limit).

Confustion2: At each energy (ev), there will have some q points (say 10 q points) dependent dielectric function. So if I define the energy range from 0 to 5 ev, would it generate the 10 q points dielectric function on each enegry (ev)? Or Would I have to run the input file considering only one Energy value on each run?

The input file you mention, in a single run, will calculate 19 response function, one for each q points, stored in a different output file. Each of them is calculated for 100 frequencies (ETStpsXd) spanning the range from 0 to 10 eV (EnRngeXd).

I hope it is now clear,

Best,

Daniele

[muhammadhasan]

Thank you for your clear reply.

Best
Jahid