How to get the surface loss function

[hplan]

Dear Developers:

I think I had made a confusion between the energy loss function and the surface loss function .
Therefore, i wonder whether yambo can do some calculations for the surface loss function ? I want to examine the plasmon dispersion of a surface, and thought it is possible to get information about surface plasmon directly from the
EELS. But after looking through literature, i found the surface loss function has a bit difference from the EELS . Would you please give me some advices ? Thank you !

Cheers,
Hai-Ping

[Conor Hogan]

Dear Hai Ping,
It depends what you mean by "surface loss function". Energy loss at a surface is far more complicated than the -Im[1/eps] form used in describing bulk loss. The simplest thing you can do is approximate your surface as a truncated bulk system with -Im[2/(1+eps_bulk)], which you could do by hand from the output of Yambo. However, probably you want something more complicated. Some functionalities for computing surface loss functions have been coded in Yambo, but are not in the GPL version. Have a look at e.g. Phys Rev B vol 79, 155447 (2009), and tell us more about how you want to calculate the loss.
Regards,
Conor

[hplan]

Dear Conor:

Thanks for your comments !

It depends what you mean by "surface loss function". Energy loss at a surface is far more complicated than the -Im[1/eps] form used in describing bulk loss. The simplest thing you can do is approximate your surface as a truncated bulk system with -Im[2/(1+eps_bulk)], which you could do by hand from the output of Yambo.

I again made a mistake and thought there was a general formula for the surface loss function.
The quantity i mentioned follows the definition by PRL 93,176801,
$-\frac{2\pi}{q}\int dz \int dz' \chi_{G=0,G'=0}(z,z',q,\omega)e^{q(z+z')}$ . This formula involves $\chi$ in a mixed basis sets, and shouldnot be directly manipulated from the output of Yambo.

However, probably you want something more complicated. Some functionalities for computing surface loss functions have been coded in Yambo, but are not in the GPL version. Have a look at e.g. Phys Rev B vol 79, 155447 (2009), and tell us more about how you want to calculate the loss.

I meant to study a metal surface with an overlayer ,and want to get some information of the plasmon dispersion . I have read your PRB work, and donot have clear understanding the relation between the formula you present and others. And i need more homework on this issue .



Thanks again.

Best wishes,
Hai-Ping

[Conor Hogan]

Dear Hai-Ping,
Well, you are right: the most general expressions for the surface loss function are indeed based on quantities of the form \chi(z,z',q,\omega). This is a complicated quantity to calculate for a real system, so people generally assume a two-layer or three-layer model for the semi-infinite dielectric function, and quantities like \epsilon(z,z') reduce to \epsilon_{bulk} and \epsilon_{surface}. You will find more information of how to make such approximations in a recent article by Hogan, Palummo, Del Sole in Comptes Rendus Physique, doi:10.1016/j.crhy.2009.03.015 (in press). I've no idea, however, if such models can predict surface plasmon dispersion correctly, however. If you want to perform a calculation like that of Silkin et al, you will need to do a lot of coding - just think about how you might compute the full \chi(q,\omega) for several different small values of q ... !

An alternative approach is to use a model of the surface plasmon dispersion suggested by Feibelman - search PRB and PRL and you will find many publications related to surface plasmon disperson on metal surfaces.

Hope it helps,
Conor

[hplan]

Dear Conor:

Thanks for your clear clarification and literature.

Well, you are right: the most general expressions for the surface loss function are indeed based on quantities of the form \chi(z,z',q,\omega). This is a complicated quantity to calculate for a real system, so people generally assume a two-layer or three-layer model for the semi-infinite dielectric function, and quantities like \epsilon(z,z') reduce to \epsilon_{bulk} and \epsilon_{surface}. You will find more information of how to make such approximations in a recent article by Hogan, Palummo, Del Sole in Comptes Rendus Physique, doi:10.1016/j.crhy.2009.03.015 (in press).

I have read your review work on EELS at surfaces , which gives me a thorough understanding on the surface loss function. I wonder why your discussion just focus on semiconductor surfaces , such as C, GaAs et al ? Is there any special consideration or limitation for extended model of EELS ?

I've no idea, however, if such models can predict surface plasmon dispersion correctly, however. If you want to perform a calculation like that of Silkin et al, you will need to do a lot of coding - just think about how you might compute the full \chi(q,\omega) for several different small values of q ... !

An alternative approach is to use a model of the surface plasmon dispersion suggested by Feibelman - search PRB and PRL and you will find many publications related to surface plasmon disperson on metal surfaces.

I have some confusions after reading your work. If the decription for dielectric properties of surface, why we can not get the correct plasmon dispersion ? In fact, i found your EELS results are quite consistent with experimental data , especially for low-energy part. I compared your implementation for surface loss function with that of Silkin et al, and found the quantity you discussed is the inverse dielectric function $\epsilon^{-1}$ rather than the response function$\chi$ involved by Silkin et al. Besides the model involved quanties, i didnot find any other difference. Therefore, why should we worry about the prediction on the plasmon dispersion ?

Best wishes

Hai-Ping

[Conor Hogan]

Dear Hai-Ping,

I have read your review work on EELS at surfaces , which gives me a thorough understanding on the surface loss function. I wonder why your discussion just focus on semiconductor surfaces , such as C, GaAs et al ? Is there any special consideration or limitation for extended model of EELS ?

Wow, that was quick.. The reason for focusing on semiconductor surfaces is just that the interband transitions can be easily studied experimentally and they have a rich structure related to the atomic reconstruction, and hence much experimental data is available in the energy region E < 10eV or so. In metal surfaces the intraband term tends to hide interband features, and are less interesting at these energies (relaxations rather than reconstructions dominate)

If the decription for dielectric properties of surface, why we can not get the correct plasmon dispersion ?

It depends on the model you refer to: the extended treatment at the end of the Comptes Rendus paper should be able to describe surface plasmon dispersion correctly, as it contains the same treatment, more or less, as that in Silkins paper. If you use a model based on a real three-layer model of the surface (like in the PRB), you introduce an arbirary definition of the "surface layer" and although this works very well for describing EELS peaks due to low energy transitions, I dont know if it will describe the dispersion ( I suspect not ).

All things considered, it depends on what you want to calculate, how accurately you want it, and how much time you are willing to spend on writing code! Yambo, in any case, cannot give you immediately what you are looking for.

Regards,
Conor

[hplan]

Dear Conor:
Thank you very much for the detailed explaination. However, i still have several questions concerned with surface
loss function implemented in yambo.

It depends on the model you refer to: the extended treatment at the end of the Comptes Rendus paper should be able to describe surface plasmon dispersion correctly, as it contains the same treatment, more or less, as that in Silkins paper. If you use a model based on a real three-layer model of the surface (like in the PRB), you introduce an arbirary definition of the "surface layer" and although this works very well for describing EELS peaks due to low energy transitions, I dont know if it will describe the dispersion ( I suspect not ).

If my understanding on this issue is correct, the central quantity you employed in the extended model is
the inverse dielectric function in a mixed basis, which is quite similar to that of Silkins' paper. Right now, i want to figure out how to make a transformation for 3D Reciprocal response function to a mixed basis. I have read several pieces of routines about wavefunction and FFT. However, I still donot have much idea how to index the reciprocal vectors, which i think is vital to 2D FFT to a mixed basis. If possible, would you please give me some advices, or your protype routines for this transformations ? I have been hindered by this problem for several weeks, I really appreciate your help and advices.

Cheers,
Hai-Ping

[Conor Hogan]

Dear Hai-Ping,
I'm sorry I can't really help you on that - everything I know is what you find in the Comptes Rendus paper. In particular the 2-D FFT are just as what appear in the paper, and were done in a non-efficient manner. You should realise that these equations are not implemented in Yambo, but in a very old version of the code, and I would not know where to start looking to be honest. If I were to write the code again, I'm sure I would do it very differently! Keep studying!
Conor

[hplan]

Dear Conor:
Thanks for your critical comments and suggestion.
Hmm, I keep reading the source code, and try to figure out the related routines.

I'm sorry I can't really help you on that - everything I know is what you find in the Comptes Rendus paper. In particular the 2-D FFT are just as what appear in the paper, and were done in a non-efficient manner. You should realise that these equations are not implemented in Yambo, but in a very old version of the code, and I would not know where to start looking to be honest. If I were to write the code again, I'm sure I would do it very differently! Keep studying!
Conor

Bests,
Hai-Ping

[Conor Hogan]

Ah - just to say, if you have a specific question about some array in the code, we can perhaps help you with that - just figure out explicitly what it is you need. It might be too difficult to explain over the forum, however, but you can try.