Why does the model interaction for Cooper pairs make sense?

In summary, the conversation is about understanding why Cooper pairs form. The textbook proof being read starts with imagining a passive electron gas and then adding two extra electrons that interact through a potential. The interaction is taken to be attractive within a narrow window above the Fermi sphere. The author is struggling to understand the reasoning behind this and is asking for insights or helpful leads. The other person clarifies that they are not questioning the presence of attraction, but rather trying to understand why this specific form of attraction is being used. The conversation ends with the author summarizing that the interaction is not operative at lower energy levels due to a filled Fermi sea, and not at higher energy levels due to the lack of available phonons. The author suggests finding another
  • #1
sam_bell
67
0
Hi All,

I am trying to understand why Cooper pairs form. The textbook proof that I am reading (Grosso & Parravicini) starts out as follows: Imagine a 'passive' electron gas filled out to some Fermi sphere kF. Add two 'extra' electrons that interact via a potential U(x-x'). Transform to k-space and take the interaction U_kk' to be attractive within a narrow window of width hωD/2pi above the Fermi sphere. This is the part where I don't follow. Why is this reasonable? Why does this make sense?

Any insights or helpful leads would be appreciated.

Thanks,
Sam
 
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  • #2
Do you mean, "why posit any attraction at all?"
 
  • #3
No, sorry, I would like to understand why the form given the attraction makes sense. It's beginning to make more sense to me. Would it be fair to say .. The interaction U_kk' for k < kFermi is not operative because of the filled Fermi sea, and not for |Ek-Ek'| >> hωD because no phonons are available to carry the energy discrepancy. Then, for simplicity, we take U_kk' = -U0 (a constant) within the window |Ek - Ek'| < hωD and zero elsewhere.
 
  • #4
That's right - remember the context is of very low temperatures so all the lower energy levels are filled.

Note: the author is simplifying the situation in the hopes that this will help you imagine the situation.
If you continue to have trouble with this, you may be well advised to find another author who uses a different approach.
 

FAQ: Why does the model interaction for Cooper pairs make sense?

1. How do Cooper pairs form in a model interaction?

The formation of Cooper pairs in a model interaction is a result of the attractive interaction between two electrons in a superconducting material. This attraction is caused by the exchange of lattice vibrations, also known as phonons, between the electrons. As the electrons interact with the lattice, they create a distortion in it, which in turn attracts other electrons and forms a pair.

2. Why is the formation of Cooper pairs important in superconductors?

The formation of Cooper pairs is crucial in superconductors because it allows for the phenomenon of superconductivity to occur. When electrons are paired up, they can move through the material without resistance, leading to the flow of electricity with zero energy loss. This is what makes superconductors highly desirable for many applications.

3. How does the model interaction for Cooper pairs explain the absence of resistance in superconductors?

The model interaction for Cooper pairs explains the absence of resistance in superconductors through the concept of electron pairing. When electrons are paired up, they form a state of lower energy known as the condensate. This condensate allows the electrons to move through the material without colliding with other particles, resulting in zero resistance and the phenomenon of superconductivity.

4. Can the model interaction for Cooper pairs be applied to all superconducting materials?

The model interaction for Cooper pairs can be applied to most superconducting materials, but there are some exceptions. In some cases, other interactions, such as magnetic interactions, can also play a role in the formation of Cooper pairs. However, the model interaction involving phonons is the most widely accepted explanation for the formation of Cooper pairs in superconductors.

5. How does the model interaction for Cooper pairs relate to the concept of electron-phonon coupling?

The model interaction for Cooper pairs is closely related to the concept of electron-phonon coupling. As mentioned earlier, the exchange of lattice vibrations (phonons) between electrons is what leads to the attraction and formation of Cooper pairs. This coupling between electrons and phonons is what allows for the phenomenon of superconductivity to occur in certain materials.

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