Vanishing fermi level and cut off value in self energy

In summary, the vanishing Fermi energy refers to a metal or graphene with all conduction electrons removed, leaving only bare ionic cores that interact via the long range Coulomb interaction. The frequency of vibrations in this case is finite and known as the plasma frequency. When electrons are added, they screen the long range Coulomb interaction, resulting in renormalized frequencies starting at 0. This means that the frequencies cannot be used in calculations for the electron-phonon interaction as they already contain this interaction. To avoid double counting, a cut off energy of half the \pi-band width is introduced. Appendix J in R. Mattuck's A Guide to Feynman Diagrams in the Many-Body Problem provides further explanation.
  • #1
Physicslad78
47
0
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 [tex]\omega[/tex]=0 and large vector k and so they introduced a cut off energy equal to half of the [tex]\pi[/tex]- band width. The reason behind that, as they say, is that this contribution is already included in the definition of the frequency [tex]\omega[/tex] 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...
 
Physics news on Phys.org
  • #2
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 [tex]\Omega[/tex]. When you add the electrons, these will screen the long range Coulomb interaction and the renormalized frequencies [tex]\omega[/tex] 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
Thanks very much for explanation...will consult the appendix...:)
 

1. What is the vanishing fermi level and why does it occur?

The vanishing fermi level refers to the point at which the fermi energy, which is the highest energy level occupied by electrons in a material at absolute zero temperature, becomes zero. This phenomenon occurs due to the depletion of electrons in the material, either through doping or by removing electrons through external processes.

2. How does the self energy affect the fermi level?

The self energy, which is a measure of the energy required for an electron to exist in a material, can cause the fermi level to shift. When the self energy is higher than the fermi level, the fermi level will shift towards the conduction band, while a lower self energy will cause the fermi level to shift towards the valence band.

3. What is the cut off value in self energy?

The cut off value in self energy refers to the maximum value of energy at which the self energy is valid. This value is usually determined by the energy range of the material being studied and can vary depending on factors such as temperature and doping level.

4. How does the vanishing fermi level affect the electrical conductivity of a material?

The vanishing fermi level can significantly impact the electrical conductivity of a material. When the fermi level is close to the conduction band, the material will have a higher electrical conductivity, while a fermi level closer to the valence band will result in a lower conductivity. The vanishing fermi level can also lead to insulating behavior in some materials.

5. Can the vanishing fermi level be controlled?

Yes, the vanishing fermi level can be controlled through various methods such as doping, applying external fields, or altering the temperature of the material. These methods can shift the fermi level and allow for the manipulation of the material's electrical and optical properties.

Similar threads

  • Atomic and Condensed Matter
Replies
0
Views
392
  • Atomic and Condensed Matter
Replies
0
Views
282
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
8
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
2K
Replies
72
Views
5K
Replies
4
Views
3K
  • Beyond the Standard Models
Replies
11
Views
2K
Back
Top