What's with 'virtual' phonons in BCS pairing?

[Creator]

Can someone explain why virtual phonons are necessary to explain BCS pairing in type I superconductors. I thought phonons originated with the lattice vibrations. I read that it s the 'virtual" phonons that explains the pairing; how so? what am I missing ?

 

[DrDu]

Real phonons are lattice deformations which can propagate freely, i.e. sound waves.
Virtual phonons are needed to describe e.g. static lattice deformations surrounding a perturbation, e.g. an electron. In the most simple limit this gives the rubber surface description of Cooper pairing: An electron behaves like a ball on a rubber surface, it creates a deformation of the surface and a second electron (ball) will fall into that hole.

 

[ZapperZ]

Can someone explain why virtual phonons are necessary to explain BCS pairing in type I superconductors. I thought phonons originated with the lattice vibrations. I read that it s the 'virtual" phonons that explains the pairing; how so? what am I missing ?

You are missing Quantum Field Theory.

The idea here is that one is trying to describe the interaction between two objects. Naively, in QFT, this is accomplished via the exchange of a virtual bosonic "particle". In E&M, it is the exchange of virtual photon. In condensed matter physics, it can be any boson that is the equivalent of a 'vacuum excitation'. In the case of conventional superconductivity, this is the virtual phonons.

In other cases, you can have an exchange of magnons, polarons, etc...

Zz.

 

[Creator]

Thank you both for the replies. So the pairing is a result mostly of the virtual phonon exchange, and not the real phonons that originate in the lattice...or both? Can either of you describe the effect of each if possible.
2. So is it the virtual momentum exchange that causes the attractive potential,?
Thanks.

 

[kimcosmos]

if quantum tunneling is involved its all virtual

 

[ZapperZ]

if quantum tunneling is involved its all virtual

No it doesn't. Show me the physics that says this.

This is also a necropost.

Zz.