Origin of Attractive Electron Interaction

In summary: Thank you for your input. In summary, the effective electron-electron interaction is not derivable from first principles, but it can be derived by using functional integrals.
  • #1
Jan Paniev
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I have started to learn BCS theory and I am not been able to find a derivation of the effective attractive electron-electron interaction which is assumed to explain the Cooper pairing. Can anyone point me to a reference where I can find this derivation?

Jan.
 
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  • #2
There is a derivation (based on second quantization) in the http://books.google.com/books?id=v5...resnum=1&ved=0CCsQ6AEwAA#v=onepage&q&f=false" by H. Bruus and K. Flensberg. Its in chapter 17 and the effective electron-electron interaction is in equation (17.16) page 316. These pages are visible at Google books.

Alternatively one can derive this result using (Feynman) functional integrals. One has to write the electron-phonon interaction term, and integrate out the photon field (which is just a Gaussian integral). Then one extra term appears which is the effective electron-electron interaction.
 
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  • #3
Thanks a lot. Although I do not have the book and I cannot see the pages, I will borrow it on Monday and take a look.

If anyone else is interested as well , some other friends also indicated me these two books

- Advanced Solid State Physics, P. Phillips
- Methods of Quantum Field Theory in Statistical Physics, Abrikosov et al.

The derivation in the first seems very simple, so I will need to take a better look to see if it is detailed enough. Abrikosov's book seems to have it in details, but I have the feeling that I will have to read almost the whole book until I can understand it...

Once more, thanks for the answer.

Jan
 
  • #4
I think that the principal mechanism is easiest to understand in the case of strong coupling. Google for "Lang Firsov transformation"
 
  • #5
Jan Paniev said:
I have started to learn BCS theory and I am not been able to find a derivation of the effective attractive electron-electron interaction which is assumed to explain the Cooper pairing. Can anyone point me to a reference where I can find this derivation?

Jan.

Actually, try looking in Ashcroft and Mermin. He showed the basic mechanism of Cooper Pairing interaction via the overscreening of the electrons.

Zz.
 
  • #7
I am checking out all the indicated books. The combination of them plus the original papers contains all the information I needed. Thanks a lot everyone for all the help. I really appreciate it!

Jan.
 

1. What is the origin of attractive electron interaction?

The origin of attractive electron interaction is the electromagnetic force, which is one of the fundamental forces of nature. This force is responsible for the attraction between negatively charged electrons and positively charged protons in an atom.

2. How does the attractive electron interaction work?

The attractive electron interaction works through the exchange of virtual particles called photons. When two electrons are close to each other, they exchange photons, creating a force that pulls them towards each other.

3. What factors affect the strength of attractive electron interaction?

The strength of attractive electron interaction is affected by the distance between two electrons, the charge of the particles, and the dielectric constant of the medium they are in. The closer the electrons are, the stronger the interaction will be.

4. Is attractive electron interaction the only force that holds atoms together?

No, attractive electron interaction is not the only force that holds atoms together. The strong nuclear force is responsible for holding the nucleus of an atom together, while the attractive electron interaction is responsible for holding the electrons in their orbit around the nucleus.

5. Can attractive electron interaction be repulsive?

Yes, attractive electron interaction can be repulsive under certain circumstances. This can happen when two electrons have the same spin and are in close proximity to each other, causing a repulsive force between them.

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