# [Wien] How to calculate Plasma Frequency and Number of effective electrons.

Zaid raheskoon at gmail.com
Fri Apr 12 09:41:10 CEST 2013

```Respected Kulpreet

I appreciate the way you explained my question. Thank you for suggesting
books.
Thank you so much.

Best Regard's
M. Zain

On Fri, Apr 12, 2013 at 3:17 PM, Kulpreet Virdi <
kulpreet.virdi at cup.uni-muenchen.de> wrote:

> Hi Zaid,
>
>
>
> yes, one way of identifying the Plasmon (energy) is the maximum in loss
> function (electron energy loss plot) however this is not always correct.
> The loss function is given by Im [-1/ε] which is equal to [ε2/(ε1^2+ε2^2)].
> In the loss function you would see a maximum when there is a local minimum
> of (ε1^2+ε2^2) or a local maximum of ε2.
>
>
>
> The local maxima of ε2 imply  interband transition(s) ; which are often
> visible in loss spectrum especially for materials containing transition or
> heavy metals. However a minima of (ε1^2+ε2^2) implies a plasmon excitation.
>
>
>
> The most often used definition of plasmon is when ε2 crosses zero [and a
> minmum of ε1^2+ε2^2 ] with a positive slope with respect to the energy
> axis. For details you can check either of these
>
>
>
> M. Fox, Optical Properties of Solids (Oxford University Press,
> Oxford, UK, 2010).
>
>
>
> V. Gallegos-Orozco, R. Martınez-Sanchez, and F. Espinosa-
> Magana, Phys. Rev. B 77, 045128 (2008).
>
>
>
> V. J. Keast, A. J. Scott, M. J. Kappers, C. T. Foxon, and C. J.
> Humphreys, Phys. Rev. B 66, 125319 (2002).
>
>
>
> I guess someone else could help you with the effective number of electrons.
>
>
>
> All the best,
>
>
>
> Kulpreet
>
> On Fri, 12 Apr 2013 12:30:09 +0800, Zaid <raheskoon at gmail.com> wrote:
>
>   Respected Wien Users
>
> I am inexperience in calculating optical properties May any one guide me
> how to calculate Plasmon energy and Number of effective electrons ? After
> some effort I came to know that the energy associated to highest peak value
> in Electron loss plot will be Plasmon energy. While value for No of
> effective electrons can be obtained from X KRAM sumrule. Can Any one
> confirm this information true ?  And which sum rule should be selected ?
>
> Best Regards
> M, Zaid
>
>
>
> ----------------------------------------
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>
>
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