Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Origin of Attractive Electron Interaction

  1. Jul 31, 2010 #1
    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.
     
  2. jcsd
  3. Jul 31, 2010 #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.
     
    Last edited by a moderator: Apr 25, 2017
  4. Jul 31, 2010 #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
     
  5. Aug 2, 2010 #4

    DrDu

    User Avatar
    Science Advisor

    I think that the principal mechanism is easiest to understand in the case of strong coupling. Google for "Lang Firsov transformation"
     
  6. Aug 2, 2010 #5

    ZapperZ

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

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

    Zz.
     
  7. Aug 2, 2010 #6
  8. Aug 4, 2010 #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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook