What are Cooper pairs from superconductors

[h1010134]

I asked about superconductors in another paost, and what I got was how superconductivity is achieved, and how electrons are attracted together via interactions with atomic nuclei. My question is, what exactly is a cooper pair? To me, when I think of the word pair, I immediately imagine the electrons as stuck together as a, well, a pair, and moving like so through the conductor. Yet, this does not help in reducing the number of collisions the electrons have with other pairs or the nuclei, which are the cause of resistance.

I don't know if this is accurate, but I got from some book that these "pairs" are not actually stuck together, but move in opposite directions and are, like, mirror images of each other. Then the book also says that if an electron in the pair hits something, theother one in the pair hits something else, such that total momentum and energy is conserved. This kinda confuses me, since for one, I have no idea how the electrons can be "linked" if they are apart i.e. one feels the effect of the other electron (this is somewhat like entanglement if I am not wrong. I do not know if it has any relation to this), and how momentum can be conserved at all if anything hits anything else - SOME energy has to be lost, right?

 

[andrien]

two electron at very low temperature can be said that they form a pair.There are lesser numbers of states available as we lower the temperature.It does not mean that they are stick to each other.It means in a rough sense that the distance between two electrons are less than their sizes.But it is rather very novel.

 

[Sonderval]

@andreien
"It means in a rough sense that the distance between two electrons are less than their sizes"
Nope. The electron wave packets are smaller than the distance between them - a cooper pair has an extension of about 100nm.

@h101...
You can consider the scattering of teh electrons as a scattering with the crystal lattice - since this is infinitely more heavy than an electron (in good approx.), the electron can change its momentum, but not its energy. (Similar to a rubberball being reflected from a wall.)
A different way of looking at the binding is to say that the binding is analoguous to the attraction of two particles by electric forces: In quantum physics, this is described by exchange of a (virtual) photon - electrons in a crystal attract via exchange of lattice vibrations (phonons).

 

[DiracPool]

A different way of looking at the binding is to say that the binding is analoguous to the attraction of two particles by electric forces: In quantum physics, this is described by exchange of a (virtual) photon - electrons in a crystal attract via exchange of lattice vibrations (phonons).

This is a fascinating topic. Couple questions: What happens to the electrons to overcome the Pauli exclusion principle (PEP)? My understanding is that the cooper pair as a unit becomes a Boson! A..wha? How does that happen? What happens to the individual spin of each electron? Does each half contribute to a "whole?" i.e., does 1/2 spin plus 1/2 spin = 1 spin boson? Or..does each electron change its spin to a spin one boson and overcome the PEP like photons do?

Two, how does simply cooling the superconductor change the spin of these electrons, and why do they form in pairs and not, say triplets, etc. I mean, they are bosons, right, we can line up millions of photons into coherent states, why just two electrons. Finally, what are the role of phonons or the "phononic effect" in this process? i.e., they have something to do with a sound-like vibration, right? Is this somehow related to the cooling effect? If so, how?

 

[andrien]

"It means in a rough sense that the distance between two electrons are less than their size"
Nope. The electron wave packets are smaller than the distance between them - a cooper pair has an extension of about 100nm.

Don't stretch my name,o.k.The statement I have written is not mine,it is given in feynman lectures and belongs to feynman.So blame him for it.By the way,What is the size of electron wave packets ?

 

[Sonderval]

@andrien
Sorry, that was just a typo, no insult intended (I was typing with cold fingers on a new desk where the keyboard is set out differently - same today, so there may be more typos...) - my apologies.
The size of typical electron-wave packets is duscissed in Ashcroft-Mermin, ch. 12 (semi-classical electron theory) - unless I misremember completely, it is of the order of a hundred lattice constants at most. However, thinking about it a bit more, it may be that this is not fully appropriate for the case of a superconductor where the k-values of the wave packet have to be strongly restricted. So perhaps I was wrong with that statement, I would need a detailed calculation of the allowed delta-k to be sure.

@DiracPool
No two electrons have the same quantum numbers. You combine one electron with wave vector +k and spin up and one with -k and spin down to a pair. All these pairs have spin 0 (not spin 1) and wave vector 0, but no two electrons have the same state.
The spin of the electrons is not changed upon cooling - it is just that there is an attractive interaction that pairs electrons with opposite spin.
The phonons are the mediators of the attractive force.
Perhaps this may be a good starting point to get some of the ideas more clearly:
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bcs.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/coop.html#c1

 

[h1010134]

As in the title, I said I understood how the pairs actually form. From the replies, I understand that these electron pairs aren't actually stuck together. Ok, but it isn't really much. Is there a more descriptive picture of what is the pair exactly?

Furthermore, if I'm not wrong, for the pair to form the electrons must travel towards each other via the attraction from the large nuclei congressing together. Like, electron--><--electron. I have another question - If this is how pairs are formed, would it be possible to cause a metal to superconduct if I put a current inside it before lowering its temperature? I.e. I cause the electrons to flow in 1 way only, as in a conventional current, then lower the temperature below the threshold. That way, would it still be possible for pairs to form?

 

[h1010134]

And, I don't really need the details, such as the electron wavepacket is smaller than somethingsomething. It doesn't help me much in understanding how the pairs work to completely conserve energy, and I consider it added details, of which I will get to after I understand the fundamentals.

@Sonderval: Ok, from what I understand from you statement, when electrons hit nuclei, which are infinitely bigger than them, energy loss is negligible and infinitely small, yes? Which is why currents in superconducting materials go on forever (or, more accurately, for an infinitely long time). My questions is, what has this got to do with Cooper pairing? In normal conductors, if the same logic is applied, will we not get negligible energy loss from collisions as well? Why would we even have resistance then?

Any response is appreciated. To note, I'm not exactly an expert on this field, and I only want to get my fundamentals straight before moving on to the math of all this. As such, do try to leave out unnecessary math and stuff. Thanks :D

 

[DrDu]

The point is not that Cooper pairs couldn't loose energy in collisions. Obviously Cooper pairs can break up in nuclear collisions and loose energy. However, the electrons produced in these collisions sooner or later will recombine and form the same Cooper pairs as before. The point is rather that due to the energy gap, the Cooper pairs themselves cannot be scattered into pair states which carry less current as there are no such states due to the energy gap.

 

[h1010134]

... Wha?! I completely did not understand anything from that

 

[DrDu]

Maybe an analogy is helpful.
Consider a paramagnet in a magnetic field. Now you suddenly change the axis of the external magnetic field. The paramagnet can relax to the new ground state by each of the spins relaxing independently.

This is analogous to electrons in a normal metal relaxing from a state with mean value of k (momentum of the electrons) to a state were mean k (and thus current) is zero.

Now if you replace the paramagnet with a ferromagnet, things are different. After changing the orientation of the external field, you can kick a single spin and change it's direction, but even if the spin points in the direction of the field afterwards, the energy of the state with the changed spin is higher than the state were it points in the same direction as it's neighbours. To reach a state of lower energy, you have to change the orientation of the majority of the spins at the same time.

This corresponds to a superconductor where all Cooper pairs have a non-vanishing value of k. When there is no driving field it would be energetically favourable for all k to be 0. However this state cannot be reached by changing the k of the Cooper pairs one by one.

 

[M@2]

As to me i want to redirect the Minich's question, he asked me, to the audience:

Do we have DIRECT experimental facts about existence of Cooper pairs?

ARPES, for example, is one electron experimental technics.
Do we have, as in particle physics, experimental evidence of electron-pozitron pair production?
Do we have real technics for registering Cooper pair production/destruction?
Coincidence events technics?

 

[ZapperZ]

As to me i want to redirect the Minich's question, he asked me, to the audience:

Who? Why are you directing this person's question on here? Are you some sort of a spirit conduit?

ARPES, for example, is one electron experimental technics.
Do we have, as in particle physics, experimental evidence of electron-pozitron pair production?
Do we have real technics for registering Cooper pair production/destruction?
Coincidence events technics?

Sure! Measure the smallest quanta of magnetic flux.

As for your attempt at thread hijacking this with off-topic question on electron-positron pair, that should be totally ignored.

Zz.

 

[M@2]

Who? Why are you directing this person's question on here? Are you some sort of a spirit conduit?

Sure! Measure the smallest quanta of magnetic flux.

As for your attempt at thread hijacking this with off-topic question on electron-positron pair, that should be totally ignored.

Zz.

Why not? I could not answer Minich's question.

I told him about yours ZapperZ's "the smallest quanta of magnetic flux". But was not unable to prove, that 1/2 quanta coudn't be acheaved by one electron theory. Minich gave simple counter example with quatization of magnetic field in the center of a ring with one electron in a ring for two body problem: one body ion lattice (ring), second body electron.

There is total inertia conservation, but there is not electron inertia conservation. Mass of a ring is determined mainly ions, so they give smallest magnetic field.
Magnetic field is determined mainly by electron velocity, so quatization is determined by delta TOTAL inertia: M*V_M + m*V_e id est equal 1/2 of "expected".

Quatization of inertia 1/2 is obtained by ION ring mass.

 

[ZapperZ]

Why not? I could not answer Minich's question.

I told him about yours ZapperZ's "the smallest quanta of magnetic flux". But was not unable to prove, that 1/2 quanta coudn't be acheaved by one electron theory. Minich gave simple counter example with quatization of magnetic field in the center of a ring with one electron in a ring for two body problem: one body ion lattice (ring), second body electron.

There is total inertia conservation, but there is not electron inertia conservation. Mass of a ring is determined mainly ions, so they give smallest magnetic field.
Magnetic field is determined mainly by electron velocity, so quatization is determined by delta TOTAL inertia: M*V_M + m*V_e id est equal 1/2 of "expected".

Quatization of inertia 1/2 is obtained by ION ring mass.

Say what?

I suppose this is what happens when 2 heads are tripping over each other trying to tackle one topic.

Every instrument that make use of such magnetic flux quanta, such as SQUIDs, are based on such 2e units. We check the integrity of materials using such devices. If you or this "Minich" person think you can do better, please submit it for publications and then build those devices using the principles you believe in. Till then, put your effort into producing such work, rather than wasting your time in a public forum to sell your ideas.

We need to get back on the OP's topic.

Zz.

 

[M@2]

ZapperZ
I've seen the paper of Minich pepared for arxiv.org. Minich is now beeng ill, has financial difficulties, but finishes paper for nature.com
So i hope everything will be done according to your advice.

How can you answer to Minich's counter example, that 1/2 quanta may be effect of ion's lattice inertia contribition?

 

[ZapperZ]

How can you answer to Minich's counter example, that 1/2 quanta may be effect of ion's lattice inertia contribition?

I have no idea what this is and what you typed earlier. Unless you can show published physics on this, it is futile to explain it on here because there is a severe language issue.

Please note that this is already off-topic to the original question. You and Minich appear to suffer from the same inability to understand the topic of a thread and insisting to interject your pet theory every chance you get. Please do not do that anymore.

Zz.