# Entanglement, Cooper Pairs And Superconductivity

lavalamp
OK, I would really appreciate it if somebody could explain to me as simply as possible why entanglement happens (between electrons), what a Cooper pair is, and what causes superconductivity.

I have read that if two electrons are entangled and something happens to one of them, it will affect the other, no matter what the separation distance is. First off, is this true? If so then that's confusing because the only forces that one can exert on the other are a tiny gravitational force, an electrostatic repulsive force and a weak nuclear force, and the effects of these rapidly decreases as distance increases (inverse square law).

I do not know what Cooper pairs are at all, I only know that they occur when Aluminium is super-cooled and becomes a superconductor.

In a ground state atom all of the electrons are in the lowest possible energy level's. Yet this does not mean that a ground state atom has no energy, I know that elctrons have spin (I don't get spin either, maybe that will be the subject of another thread) and angular momentum etc. so to lose even more energy, an atom could lose the angular momentum and spin that the electrons have. And eventually after losing enough energy it may even reach absolute zero.
Sometimes though, once the temperature of a particular group (albeit a very large group) of atoms has dropped below a certain temperature, it can becomes a superconductor and an electric current can be passed through it without experiencing any resistance. This is really befuddling.
I thought that when an electron traveled down a wire, it might "bump" into an atom and lose some energy to an electron which would be promoted to a higher energy level, then when it dropped back down again it emitted a photon (usually infra-red).
So how does a superconductor work and why?

It would be really nice of someone to answer just one of these questions, although please don't bury me in mathematical equations that I won't know, I only want to know the theory behind why these things work.
An analogy may also help if you can dream one up, for instance I like to think of Higgs particles as treacle that slows stuff down.

futz
Once a superconductor is cooled below its critical temperature, its reistance drops to 0. This coincides with the production of Cooper pairs, as you mentioned. As the name suggest, a Cooper pair is two electrons, which "join" in such a way that the total spin cancels out. In this way, a Cooper pair behaves like a single particle with spin 0 and mass twice that of a single electron.

Electrical resistance in a material is due for the most part to scattering of electrons off of atoms in the material. In a SC, we have pairs scattering instead. One way to think about it is this: two electrons "attached" together is harder to affect than a single one, so it is less likely to scatter, reducing the resistance.

Technically, the quantum mechanical wavefunction of each Cooper pairs have to be identical in order to maximize the energy reduction due to attractive interactions (that is, the binding energy of a Cooper pair is greatest when all pairs are in the same state). This is known as "cooperative phenomenon". Scattering of a Cooper pair would change its wavefunction; this would necessarily require all pairs to change as well (their binding energy would drop).

All pairs would be in the same state at 0 K. At finite temperature greater than 0, some pairs are broken up due to thermal excitations.

BTW, all of this is due to something called BCS theory, which applies very well for elemental (Type I) superconductors. For high temperature superconductors (such as YBCO) it doesn't necessarily apply as well.

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lavalamp
That actually makes a lot of sense, I was expecting something horendously complicated. Thank-you for taking time out to explain that to me.

However, one small point. When there are two electrons in a sub-shell together (say in a helium atom), they have opposite spins already, so how do they differ from a Cooper pair?

I understand that the binding energy sort of acts like an attractive force in that the electrons don't have enough energy to separate, but how can the electrons affect each other no matter what the distance is between them? Surely the less energy that the electrons have, the smaller the maximum separation distance could be.

futz
Originally posted by lavalamp
That actually makes a lot of sense, I was expecting something horendously complicated. Thank-you for taking time out to explain that to me.

However, one small point. When there are two electrons in a sub-shell together (say in a helium atom), they have opposite spins already, so how do they differ from a Cooper pair?

I understand that the binding energy sort of acts like an attractive force in that the electrons don't have enough energy to separate, but how can the electrons affect each other no matter what the distance is between them? Surely the less energy that the electrons have, the smaller the maximum separation distance could be.

Two electrons in a Cooper pair are bound together and behave like a single particle. Two electrons in He can still be treated as individual particles.

lavalamp
I read the whole page and found it to be very informative, especially sections c3 and c4. I think the diagram really helped things along.

If the electrons are separated by a distance of 100nm though, how will opposite spins lower the energy, I thought that was only good for lowering energy when the electrons are confined. I suppose that 100nm is pretty confined but not compared to 0.1 - 0.4 nm.

heumpje
That is because the actual mechanism behind superconductivity is not in the spin part. It's rather that there exists an attractive force between electrons. This force comes from the interaction between the lattice and the electrons: the so-called electron-phonon interaction. Instead of repelling each other, the electrons in a superconductor attract each other.