## the infinite frequency permittivity

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.
Weiqing Zhou
Posts: 48
Joined: Thu Sep 06, 2018 7:57 am
Location: Wuhan University

### the infinite frequency permittivity

Hi all,

Can I obtain the infinite frequency permittivity \epsilon_{\infty} from Yambo? It is worth noticing that \epsilon_{\infty} is not the permittivity at infinite frequency, which should be 1. Static function comes from two contributions from electrons and ions. The summation of these two should be the lattice static dielectric constant. The only contribution of electrons should be the infinite dielectric constant.

Best,
Weiqing
Weiqing Zhou
Phd student
Wuhan University
Wuhan, Hubei, 430072

Daniele Varsano
Posts: 2719
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: the infinite frequency permittivity

Dear Weiqing,
the epsilon yambo calculates provides the electronic contribution only as ionic part it is not taken into account.
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/

Weiqing Zhou
Posts: 48
Joined: Thu Sep 06, 2018 7:57 am
Location: Wuhan University

### Re: the infinite frequency permittivity

Dear Daniele,

Thanks for reply!

So, the first value of yambo output Re[\epsilon(\omega=0)] is \epsilon_{\infty} ? From experiment, \epsilon_{\infty} is estimated as ~ 7. But in Yambo, Re[\epsilon(\omega=0, q=0)] is ~ 300. Can yambo calculate static dielectric function of metal correctly?
Notice that : The problem is not about Drude term, \epsilon_{\infty} should be estimated without Drude term. and I use 80 Ry and 49*49*21 k-points grid in DFT, and I don't think the problem is about DFT part.

b.t.w. can I plot non-interacting response function χ(q,ω= 0) and coulomb interaction v(q) separately?

Best,
Weiqing
Weiqing Zhou
Phd student
Wuhan University
Wuhan, Hubei, 430072

claudio
Posts: 320
Joined: Tue Mar 31, 2009 11:33 pm
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### Re: the infinite frequency permittivity

Dear Weiqing,

you can calculate the dielectric constant for different q using the QpntsRXd variable.
Yambo will produce different files, one for each q-point.
Then in columns 3 and 4, you can find the imaginary and real part of the non-interacting dielectric constant
that is related to the x(q,w=0)

best
Claudio
Claudio Attaccalite
[CNRS/ Aix-Marseille Université/ CINaM laborarory / TSN department
Campus de Luminy – Case 913
13288 MARSEILLE Cedex 09
web site: http://www.attaccalite.com
Freely download scientific books from: http://www.freescience.info

Daniele Varsano
Posts: 2719
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: the infinite frequency permittivity

Dear Weiking,
let me add that I've the impression that Re[\epsilon(\omega=0)] for metals, even if omitting the Drude term will strongly depend on the q point sampling.
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/

Weiqing Zhou
Posts: 48
Joined: Thu Sep 06, 2018 7:57 am
Location: Wuhan University

### Re: the infinite frequency permittivity

Dear Daniele，

If I don't add DrudeWd, only interband transition would be taken into account even if the system is a metal? Is that right?

Best,
Weiqing
Weiqing Zhou
Phd student
Wuhan University
Wuhan, Hubei, 430072

claudio
Posts: 320
Joined: Tue Mar 31, 2009 11:33 pm
Contact:

### Re: the infinite frequency permittivity

Yes this is right

Claudio
Claudio Attaccalite
[CNRS/ Aix-Marseille Université/ CINaM laborarory / TSN department
Campus de Luminy – Case 913
13288 MARSEILLE Cedex 09
web site: http://www.attaccalite.com
Freely download scientific books from: http://www.freescience.info

Daniele Varsano
Posts: 2719
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: the infinite frequency permittivity

Dear Weiqing Zhou,
I would say no, if you do not include the Drude contribution you do not have the intraband contribution in the q->0 limit, but for finite q vectors intraband contributions of the metallic bands are included.

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/

Weiqing Zhou
Posts: 48
Joined: Thu Sep 06, 2018 7:57 am
Location: Wuhan University

### Re: the infinite frequency permittivity

Dear Daniele,
if you do not include the Drude contribution you do not have the intraband contribution in the q->0 limit, but for finite q vectors intraband contributions of the metallic bands are included.

I check the asymptotics of \epsilon_{infty} where \epsilon_{infty} should be \frac{1}{q^{2}} at q→0 in 3D. From the asymptotics of finite q (see fig in attachment), I can extrapolate the \epsilon_{infty} at q=0 is 230.

I doubt that intraband contributions of the metallic bands is the reason why \epsilon_{infty} calculated is much higher than that of experiment.
Can I eliminate all intraband contributions and obtain a "clean" interband dielectric function?

Weiqing
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Weiqing Zhou
Phd student
Wuhan University
Wuhan, Hubei, 430072

Daniele Varsano
Posts: 2719
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: the infinite frequency permittivity

Dear Weiqing,
Can I eliminate all intraband contributions and obtain a "clean" interband dielectric function?
No this is not possible, what you can do is to reduce the electronic temperature to somehow reduce the metallicity but I doubt it will work.
Just a question, but are you looking at the IP reposnse funcion or the irreducible X:
X=X^0+X^0+vX
as in this case the macrsocopic dielectric function would be :
1/eps_00^-1 which is different from eps_00

In other words, have you tried to include local field effects?

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/