Origin of Attractive Electron Interaction

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Discussion Overview

The discussion revolves around the derivation of the effective attractive electron-electron interaction in the context of BCS theory, particularly as it relates to Cooper pairing. Participants seek references and resources that provide a detailed explanation of this concept, exploring various theoretical approaches and literature.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests references for the derivation of the effective attractive electron-electron interaction in BCS theory.
  • Another participant suggests a specific book by H. Bruus and K. Flensberg, indicating a relevant chapter and equation for the derivation.
  • It is mentioned that the derivation can also be approached using functional integrals, specifically through the electron-phonon interaction term.
  • Additional book recommendations are provided, including "Advanced Solid State Physics" by P. Phillips and "Methods of Quantum Field Theory in Statistical Physics" by Abrikosov et al., with varying levels of complexity noted.
  • A participant suggests that the principal mechanism of the interaction is clearer in the case of strong coupling and references the "Lang Firsov transformation."
  • Another participant points to Ashcroft and Mermin's work, which discusses the Cooper pairing interaction through the concept of overscreening of electrons.
  • A later reply mentions Annett's book as another source for the derivation.

Areas of Agreement / Disagreement

Participants generally agree on the need for references and resources for understanding the derivation, but there are multiple suggested approaches and sources, indicating a lack of consensus on a single definitive reference.

Contextual Notes

Participants express varying levels of familiarity with the suggested texts and methods, indicating that understanding may depend on prior knowledge and the complexity of the materials.

Who May Find This Useful

This discussion may be useful for students and researchers interested in BCS theory, particularly those seeking to understand the theoretical foundations of Cooper pairing and related electron interactions.

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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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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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
 
I think that the principal mechanism is easiest to understand in the case of strong coupling. Google for "Lang Firsov transformation"
 
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.
 
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.
 

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