GW in metals

[juanma]

We are performing calculations about the HOMO-LUMO changes of benzene on metallic and semiconductor surfaces (physisorbed). The results for the semiconductor are consistent with our model, but it is not the case with the metals.

In your recent paper about Yambo you say that Plasmon pole approximation for metals is not as good as for the semicinductors. Why is this?

Thank you in advance,

Juanma

[Daniele Varsano]

Dear Juanma,
Andrea is going to answer you in detail about the reliability of the aproximation,
anyway I would like to point to your attention this paper about GW for
moelcules physisorbed at surfaces and polarization effects that enters in the calculations,
it could be useful for your work:


6. J. B. Neaton, M. S. Hybertsen, and S. G. Louie, "Renormalization of molecular electronic levels at metal-molecule interfaces", Phys. Rev. Lett. 97, 216405 (2006)

Cheers,

Daniele

[andrea marini]

Dear Juanma,

you are indeed correct. Although it is not possible to affirm that, in general, for any metalsth Plasmon Pole approx (PPA) is not suitable, we can always say that in metals the breakdown of the PPA is more easily observed. The reasons can be understood by looking at the analytic expression of the self-energy (mass operator) posted here

PIC_doc_GW-42.png

From this expression we see that if you want to evaluate the GW corrections for a state with energy E, then the mass operator M(E) will have poles at the energies E-E'-Omega. Where E' is any other single particle state and Omega is the plasmon frequency.

Now, that key assumption in the PPA is that the plasmon frequency must be large enough such that E-E'<<Omega. This is because the plasmons introduced in the PPA are not physical, they represent only a fit of the real RPA inverse dielectric function. So you do not want the poles of the mass operator to fall within the bands you want to calculate GW corrections for.

Now, in semiconductors the plasmon frequency is generally large, and, in any case, it is larger then the gap. In metals instead the gap is zero, and the PPA plasmon energies may be too small. Silver for example, is a well known pathological case where the zero momentum plasmon energy is 4 eV !

So, in conclusion, to be sure that the PPA will fail for your metal have a look at the peaks in the ineverse dielectric function as a function of the transferred momenta (o*eel* obtained by using "yambo -o c"). If you see peaks with an energy lower then the band width of you metal, then you know that the PPA may fail.

Let me know if you need further clarifications

[hplan]

Dear Andrea:
I also have some confusions about the reliability of PPA in self-energy calculations.

you are indeed correct. Although it is not possible to affirm that, in general, for any metalsth Plasmon Pole approx (PPA) is not suitable, we can always say that in metals the breakdown of the PPA is more easily observed. The reasons can be understood by looking at the analytic expression of the self-energy (mass operator) posted here

PIC_doc_GW-42.png

In your thesis, you ascribe the failure of PPA for Cu metal to the flat d-bands around Fermi-level(Page 66). Therefore, my confusion is whether PPA holds for s-metal such as Na/Ca/K et al, since s-states are quite dispersion around fermi level. I donot understand well for this point though you claimed that such bands result of strong transitions in $\epsilon^{-1}$ for a large energy range. In this sense, i think we can also judge the reliability of PPA to examine $\epsilon^{-1}$ .

So, in conclusion, to be sure that the PPA will fail for your metal have a look at the peaks in the ineverse dielectric function as a function of the transferred momenta (o*eel* obtained by using "yambo -o c"). If you see peaks with an energy lower then the band width of you metal, then you know that the PPA may fail.

Does this scheme also hold for us to do judgements on semiconductors ?


Regards,
Hai-Ping

[andrea marini]

Dear Andrea:
In your thesis, you ascribe the failure of PPA for Cu metal to the flat d-bands around Fermi-level(Page 66). Therefore, my confusion is whether PPA holds for s-metal such as Na/Ca/K et al, since s-states are quite dispersion around fermi level.

Dear Hai-Ping, if the NA/Ca/K plasmons are located far from the Fermi level, at a distance larger then the energy of the level you want to calculate the QP corrections for, then the PPA may work.

So, in conclusion, to be sure that the PPA will fail for your metal have a look at the peaks in the ineverse dielectric function as a function of the transferred momenta (o*eel* obtained by using "yambo -o c"). If you see peaks with an energy lower then the band width of you metal, then you know that the PPA may fail.

Does this scheme also hold for us to do judgements on semiconductors ?

Yes. It does.