# Vanishing fermi level and cut off value in self energy

1. Feb 2, 2010

Guys, I have two questions:

(1) what does a vanishing Fermi energy mean?

(2) I have also calculated the phonon self energy for the electron phonon interaction in graphene. However in one of the papers, they state that one needs to subtract from this self energy the case of vanishing Fermi level and Born oppenheimer approximation ( where $$\omega$$=0 and large vector k and so they introduced a cut off energy equal to half of the $$\pi$$- band width. The reason behind that, as they say, is that this contribution is already included in the definition of the frequency $$\omega$$ in graphene and has to be taken off to avoid double counting. Can anyone give me an idea of why this is the case...

Thanks...

2. Feb 2, 2010

### DrDu

Well, consider a metal (or graphene) with all the conduction electrons removed. Then you are left with the bare ionic cores which interact via the long range Coulomb interaction.
The vibrations will therefore start like plasma oscillations at a finite plasma frequency $$\Omega$$. When you add the electrons, these will screen the long range Coulomb interaction and the renormalized frequencies $$\omega$$ starting at 0 will result. So you cannot use these frequencies in the calculation of the electron-phonon interaction as they already contain the electron-phonon interaction.
Maybe, appendix J in R. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, Dover Publ. is helpfull.

3. Feb 2, 2010