Talk:Cooper pair

Copyright violation
This page appears to be copied completely from http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/coop.html. According to the Copyright info on this page it's not allowed to just be copied, but the author seems open to licencing for educational purposes, which might include Wikipedia. Do we have permission, or does anyone feel like asking? --Apyule 06:54, 3 October 2006 (UTC)

Copyright violation resolved. Good catch! Nbishop 03:36, 17 October 2006 (UTC)

Densitiy of carriers
How can the electrons be 100 nm apart? Mercury is a metal. It has a lot electrons at the fermi energy. Arnero 21:40, 4 December 2006 (UTC)

There are a lot of electrons between two which form a cooper pair; the distance of 100-1000nm refers to the two electrons which form a pair. Even though it is hard to imagine, cooper pairs are a lot larger than the average distance between cooper pairs, or individual electrons for that matter. --Jonasbinding 12:41, 24 August 2007 (UTC)

Cooper paired electrons are only a small portion of the electrons at the fermi energy. The "sphere of influence" (or whatever you want to call it) of a cooper pair is 100nm-1000nm, but within that sphere there are many other (10^6?) other cooper pairs. (Their spheres overlap.) If you tried to find the location of the specific electrons comprising a given cooper pair, their "probability cloud" is large. —Preceding unsigned comment added by 205.250.252.133 (talk) 06:01, 2 June 2009 (UTC)

Comparison
How is this binding related to Covalent bond or Van der Waals forces ? Arnero 21:40, 4 December 2006 (UTC)

Covalent and VdW bonds refer to how electrons bind atoms together. A cooper pair refers to how Phonons bind two electrons together, which would otherwise move relatively free inside a metal. --Jonasbinding 12:41, 24 August 2007 (UTC)

Simplification?
Does the following phrase really belong in a section called "A simplified explanation"?

"...consider that many quasiparticles are more localized in K-space than in the usual space."

Orphan line?
What does "The pair are still Cooperic if k1 = k2 and k1 − q = − (k1 − q) = − ( − k2 − q) = − (k2 + q)" mean? This is the only time that those letters are used - it feels like this is an orphan from a previous edit. Alec.brady 09:42, 7 June 2007 (UTC)

Looking at the history, it's not left from an old edit, but it does feel like an orphan line and doesn't fit into the article. k1 and k2 presumably refer to the wave vectors of the electrons, q to a phonon they exchange (standard notation); but I'm not familiar with the statement itself, so I don't feel capable of improving it. I'd take it out; it's certainly a rather special case which doesn't fit the rest of the article. --Jonasbinding 12:41, 24 August 2007 (UTC)


 * I came here to ask about this. Apparently it has been here for more than two years. 72.75.67.226 (talk) 09:55, 6 October 2009 (UTC)


 * Agreed. It's gone now.  If anybody puts it back, please add some sort of amplification. Nibios (talk) 20:33, 7 November 2009 (UTC)

Removed article "Cooper electron pair"
I've removed the article "Cooper electron pair", on the grounds that it's a duplicate of this article and has had a merge tag on it for over a year! The content of that article was as follows:


 * A Cooper (electron) pair is a quasi-bound state of a pair of two electrons in a superconducting material. The composite entity behaves as a particle, with zero spin and charge twice that of an electron. Cooper pairs carry the current in a superconductor. This effect is most known concerning superconductivity.


 * A Cooper pair can form in a metal at low temperature. Despite the fact that the electrons Coulomb-repel each other, it may be possible to get an overall attractive force between the two. This is commonly explained in terms of an indirect coupling between the electrons, mediated by the lattice of positive ions.


 * Cooper pairs are an integral part of the theory of low-temperature superconductors, BCS theory.

I don't think there's any additional information in this text that isn't already in the Cooper pair article, but others' views would be useful here. I wonder whether the first sentence or two would make a better (well, simpler for the non-expert reader) introduction to the Cooper pair article than what's currently used. Djr32 (talk) 22:06, 8 November 2008 (UTC)


 * Good job deleting the duplicate article, looks completely redundant to me. I agree something like the first paragraph (excluding the awkward last sentence) would make a better lead-in for nontechnical readers than what's there now.  Go ahead.  -- Chetvorno TALK 00:56, 9 November 2008 (UTC)

"Walking electrons" explanation
If the chemical linkage between copper (and other) conductive atoms were considered to the linkage between an electron between two adjacent atoms, we would have a linked two electron unit which sounds like a Cooper pair. Now if one end of that paired electron system would broken loose due to agitation of the odd Z atoms we would have a loose electron which would be inclined to move in the downstream direction of the field gradient. Then at some point it would be restrained by it's connection to the retained electron link. Then if, by an additional expenditure of energy the retarding link could be broken, we could then imagine a kind of "walking" action of the paired electrons in the downstream direct of the electric gradient. Finally, if we could imagine that both ends of the paired electric linkage system could get loose under low kinetic energy conditions, we could imagine the existence of a loose but linked pair of electrons which could float in the direction of the electric gradient, with no amount of energy input being required for the flow of current process. Can your imagination handle that? We could call it the "Walking electrons concept".WFPM (talk) 05:41, 25 April 2010 (UTC)Thank you8!

Now as I was going to say before I interrupted myself, We can have a concept of a current flow (in the wrong direction) as being a flow of paired and linked electrons in a conductive circuit. And that might be significant because of what happens as a result of that occurr4ence. When an electron flow occurs in a circuit, the cylindrical surrounding volume of space becomes occupied by an "Electromagnetic Field" which contains an amount of energy and maybe inertia related to the rate of the motion of the moving electron system. And if we imagine a material entity that could make up the constituency of that electromagnetic field, we might be better able to understand it. And do we have a concept of an entity that could exist in space and contain energy? Strangely enough we do. It's a a particulate constituent of the light quanta concept, where energy is moved in discrete energy packages called quantum, and the quantum itself can be considered to be a package of smaller entities. And if we consider a particle that carries a Planck's constant amount of energy and call it a Planck particle we would have a 10 to the - 47th gram particle that could exist and float around in space. And the electromagnetic field would be merely an organized system of these particles which is managed by the energy system controlling the flow of the electrons in the electric circuit. I'm afraid I can't describe this concept mathematically and would welcome any help I can getWFPM (talk) 16:46, 25 April 2010 (UTC) My only quantitative concept is that the planck particle should have enough mass and kinetic energy to be able to transfer a planck's value amount of energy when moving at the velocity of light.WFPM (talk) 18:05, 25 April 2010 (UTC)

Spin and bosonic properties
What is the spin of a cooper pair, 0 or 1?

As a composite boson, what bosonic properties it does not possess? —Preceding unsigned comment added by 109.65.8.152 (talk) 04:22, 16 July 2010 (UTC)

''Composite bosons do not follow the usual Bose-Einstein statistics. The statistics for composite bosons made of two fermions has to take into account the underlying Fermionic nature (via Pauli principle).'' —Preceding unsigned comment added by 83.206.8.145 (talk) 09:30, 10 March 2011 (UTC)

Relation with superconductivity
The two sentences in Bold in the following paragraph are false :

''Cooper originally just considered the case of an isolated pair forming in a metal. When one considers the more realistic state consisting of many electrons forming pairs as is done in the full BCS Theory one finds that the pairing opens a gap in the continuous spectrum of allowed energy states of the electrons, meaning that all excitations of the system must possess some minimum amount of energy. This gap to excitations leads to superconductivity, since small excitations such as scattering of electrons are forbidden.[6] The gap appears due to many-body effects between electrons feeling the attraction.''

i) The gap to excitations is not itself responsible for superconductivity : for example, a hard-gap in the Density-Of-states simply reflects the absence of quasi-particle excitations in a certain energy range and leads to a (very strong) insulating behavior.

ii) The second sentance is even more false : the gap reflects the attraction between two electrons that form a pair. This naturally leads to a gap in the ONE-particle density-of-states. This is a two-body effect and not a many body effect. What reflects the many-body effect are the coherence peaks at the gap edges. These peaks highlight the difference between a simple gap (no single particle excitations below a certain energy) and the superconducting gap with long-range coherence, which is indeed a many-body effect.

In order to create a magnetic field, wouldn't it be necessary for the conducting electrons to find a "tunnel" within the unit cell through which they could float (2 at a time?) without resistance? So wouldn't the unit cell structure have to be consistent with such a path?WFPM (talk) 22:53, 4 May 2011 (UTC)

the myth of composite boson condensation
I know this is often said and written, but it must be wrong nevertheless:


 * "Electrons have spin-​1⁄2, so they are fermions, but the total spin of a Cooper pair is integer (0 or 1) so it is a composite boson. This means the wave functions are symmetric under particle interchange. Therefore, unlike electrons, multiple Cooper pairs are allowed to be in the same quantum state, which is responsible for the phenomena of superconductivity."

If this were true, there would be no degeneracy pressure and no neutron stars; the neutrons would form pairs and collapse into a black hole. The Pauli exclusion principle isn't suspended; the wave function is still antisymmetric under exchange of the individual fermions; if two composite bosons were in the same state, it would be zero.

Perhaps someone who has a better understanding of the correct explanation than I do could fix this? --Joriki (talk) 17:32, 25 October 2018 (UTC)
 * It is indeed expected that neutrons can form Cooper pairs inside neutron stars, leading to superfluidity (see references in this article). 50.71.134.166 (talk) 04:36, 18 December 2020 (UTC)
 * I do agree that it isn't so obvious, and I don't know it well enough to explain. He4 becomes superconducting as the superfluid forms, and doesn't reduce to zero density, or anything strange like that. He3 becomes superfluid at a much lower temperature. As I understand it, He3 can move easily through superfluid He4. In any case, it seems to me that neutron stars have to be cold enough, as with electrons and He3, for superfluidity to occur. But also that not all the neutrons will go into the superfluid state, so it will still not completely collapse. Gah4 (talk) 10:17, 18 December 2020 (UTC)
 * I do agree that it isn't so obvious, and I don't know it well enough to explain. He4 becomes superconducting as the superfluid forms, and doesn't reduce to zero density, or anything strange like that. He3 becomes superfluid at a much lower temperature. As I understand it, He3 can move easily through superfluid He4. In any case, it seems to me that neutron stars have to be cold enough, as with electrons and He3, for superfluidity to occur. But also that not all the neutrons will go into the superfluid state, so it will still not completely collapse. Gah4 (talk) 10:17, 18 December 2020 (UTC)
 * I do agree that it isn't so obvious, and I don't know it well enough to explain. He4 becomes superconducting as the superfluid forms, and doesn't reduce to zero density, or anything strange like that. He3 becomes superfluid at a much lower temperature. As I understand it, He3 can move easily through superfluid He4. In any case, it seems to me that neutron stars have to be cold enough, as with electrons and He3, for superfluidity to occur. But also that not all the neutrons will go into the superfluid state, so it will still not completely collapse. Gah4 (talk) 10:17, 18 December 2020 (UTC)

useful addition, regarding new states of matter ?
X1\ (talk) 01:04, 19 November 2019 (UTC)

tunneling
Should there be some discussion of tunneling of pairs? Actually, I got interested in the question from alpha decay, in which bound states of protons and neutrons tunnel out of a nucleus. How is it that they manage to tunnel together? Pretty much the same way that Cooper pairs do. Gah4 (talk) 00:32, 2 October 2020 (UTC)