[Wien] How to find the exact value of infinte epsilon?

[Gavin Abo]

There is the relation [1]:

λ = hc/E

Then with that:

λ = limit_{E→0} [hc/E] = ∞

I seem to be missing what you defined epsilon_0 and epsilon_oo as.

There is ε0 defined as the dielectric constant at low frequency and ε∞ 
the dielectric constant at high frequency like in equation (18) of [2],

where ε0, ε(0), or εs might be also be known as the static electric 
constant while ε∞ the optical dielectric constant as given in section 
"Debye relation" on page 12 in [3].

Or the epsilon_0 as defined as ε1(0), where ε1(ω) is the real part and 
ε2(ω) is the imaginary part of the dielectric function like in equation 
1 of [4]:

ε(ω) = ε1(ω) + iε2(ω)

where it may be that ε1(0) and ε1(∞) are given by equations 144 and 145 
seen in [5].

Equation 5 in [4] has

ε1(ω) ∝ Integral{ε2(ω)}

where in equation 3 of [4]

ε2(ω) ∝ Integral{δ(energy)}

I believe it was article [6] where equations such as 2.26 are used by 
WIEN2k [7,8] that seems to correspond to equation 5 in [4].

The energy you are referring to is ћω in equation 2.19 of [6] (or 
equation 3 in [4]) unless I missed something and it is another energy 
that is being talked about.

[1] 
https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation#Spectral_forms
[2] http://www.lajpe.org/sep14/03_LAJPE_928_Sagadevan_Suresh.pdf
[3] 
https://assets.testequity.com/te1/Documents/pdf/keysight/dielectric-measuring-basics-an.pdf
[4] https://arxiv.org/abs/1909.11419v1
[5] 
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.718.9681&rep=rep1&type=pdf
[6] https://arxiv.org/abs/cond-mat/0402523v1
[7] http://www.wien2k.at/events/ws2006/Optics_Vienna_April_2006.pdf
[8] http://www.wien2k.at/events/ws2008/talks/Ambrosch-Optics.pdf

On 11/29/2021 11:30 PM, Fecher, Gerhard wrote:
> What is the wavelength at zero energy ?
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Physics
> Johannes Gutenberg - University
> 55099 Mainz
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Atefe Marasi [13marasi at gmail.com]
> Gesendet: Montag, 29. November 2021 23:25
> An:wien at zeus.theochem.tuwien.ac.at
> Betreff: Re: [Wien] How to find the exact value of infinte epsilon?
>
> Dear Xavier
>
> Thank you for your prompt reply.
>
>> Infinite epsilon means that you extrapolate ...
> Do you mean that infinite epsilon (epsilon_oo) is nothing more than epsilon zero (epsilon_0)?
>
>> You must plot the real part...
> I have plotted the real part of epsilon in z direction(for BaTiO3), as would be seen from the following link:
> https://imgurl.ir/uploads/p793339_infinite_epsilon.jpg
> As expected, the above figure shows that the real part of the epsilon tends to unity at high frequency. From this plot, the epsilon_0 is about 6.5, but I am still not sure that whether infinite epsilon is really equal to epsilon_zero (epsilon_oo =? epsilon_0).
>
>> You must be careful because if you have a band gap and a bad description of the gap value ...
> Thank you for this hint. I will try to obtain a suitable band gap by TB-mBJ functional. However, at this step, I need to find out the difference between epsilon_oo and epsilon_0. In my opinion, which I am not sure about it, epsilon_00 would be evaluated at infinite energy, while epsilon_0 would be evaluated at zero energy, as deduced  from their names.
> Thank you for your nice cooperation.
>
> Best Regards
> Atefe Marasi
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