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Confuse with the formation of cooper pairs

by paulzhen
Tags: confuse, cooper, formation, pairs
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paulzhen
#1
Nov1-13, 02:06 AM
P: 23
Hi all,

There are 2 points I do not get:

1. I read something saying that phonon is an energy packet of "heat and sound", and propagates through lattice vibration...so, I thought it is saying that phonon is emitted by one electron, then absorbed by the lattice (and excited one of its vibration mode), then (the phonon) re-emitted via vibration, finally absorbed by another electron.
But when I read on, I found that the electron-phonon interaction is a direct process between 2 electrons (one emitted a phonon, another one immediately absorbed it, nothing to do with lattice). So what is the role of "lattice vibration" playing in this phonon exchanging process? Or what exactly is "phonon exchange between electrons"?

2. How can it possible that "a cooper pair travel in one direction, but 2 electrons have opposite momenta (means travelling in opposite direction)"? Just desperately asking...how can this happened?

Thanks so much for helping!!
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K^2
#2
Nov1-13, 03:54 AM
Sci Advisor
P: 2,470
It's field theory stuff. You have electron interacting with particles in the lattice. The total of these interactions can be written as if a quaziparticle, a phonon, is emitted or absorbed by an electron. So yes, first electron interacts with the lattice, and the lattice interacts with the second electron. But since we are only interested in interactions due to excitation of lattice, we can write it as particle emitted by first electron and absorbed by second.

As for the propagation of pair, in simplest way, think of it as center of mass motion. Center of mass can be moving in a particular direction, while the two particles move in opposite directions with slightly different momenta. Reality is a bit more complicated, since electrons themselves are delocalized, but it's the same principle.
paulzhen
#3
Nov1-13, 08:20 AM
P: 23
Quote Quote by K^2 View Post
It's field theory stuff. You have electron interacting with particles in the lattice. The total of these interactions can be written as if a quaziparticle, a phonon, is emitted or absorbed by an electron. So yes, first electron interacts with the lattice, and the lattice interacts with the second electron. But since we are only interested in interactions due to excitation of lattice, we can write it as particle emitted by first electron and absorbed by second.

As for the propagation of pair, in simplest way, think of it as center of mass motion. Center of mass can be moving in a particular direction, while the two particles move in opposite directions with slightly different momenta. Reality is a bit more complicated, since electrons themselves are delocalized, but it's the same principle.
Thanks for your answer!
For the second part, since 2 electrons have opposite momenta, does it imply that they just "pair" with each other for a short term (say within coherence length?), and will change their "partner" consistently?

DrDu
#4
Nov1-13, 02:17 PM
Sci Advisor
P: 3,550
Confuse with the formation of cooper pairs

The two electrons forming a Cooper pair have only opposite momenta if there is no current flowing. If there is a superconducting current, the momentum of the two electrons adds up to the average momentum of the Cooper pairs.


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