Hey all,
Just a question in class today about how the interaction between electrons can be strong even though they are moving in opposite directions. Remember that in classical superconductors the electron-electron interaction is mediated by phonons. I.e. the actual paring interaction is electron-phonon interaction. An electron can interact with the phonon field at any point in space. This interaction can propagate in the phonon field until it reaches the other electron (i.e. the only electron with the exact opposite wave vector sign and spin) when it interacts with it. Giving an effective long distance paring between the two spatially separated electrons.
This is kinda similar to what we have been doing in quantum with the field interactions. I.e. we have an electron field interacting with a phonon field. Giving effective electron, electron interactions mediated by a virtual phonons.
Just a question in class today about how the interaction between electrons can be strong even though they are moving in opposite directions. Remember that in classical superconductors the electron-electron interaction is mediated by phonons. I.e. the actual paring interaction is electron-phonon interaction. An electron can interact with the phonon field at any point in space. This interaction can propagate in the phonon field until it reaches the other electron (i.e. the only electron with the exact opposite wave vector sign and spin) when it interacts with it. Giving an effective long distance paring between the two spatially separated electrons.
This is kinda similar to what we have been doing in quantum with the field interactions. I.e. we have an electron field interacting with a phonon field. Giving effective electron, electron interactions mediated by a virtual phonons.
Regarding the coupling of the spin, wasn't there something to do with thinking about this in k-space?
ReplyDeleteThey're related in k-space, just not real space?
So when every conducting electron pairs up with another electron with the exact opposite wave vector sign and spin via the phonon field we get a Cooper pair which is a boson. I am still not sure how it helps to create a current without any resistance. Most articles I have read before just say something along the lines that "when you have a lot of these pairs and their wavefunctions overlap they form a condensate (BEC) and can travel without resistance." without going into further detail.
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