# Superconductivity - Cooper Pair

what_are_electrons
How far apart in space are these electrons?
Are the spins truly up and down or do they have the same spins (parallel)?
If they are up and down paired, then what causes that orientation?

Related Quantum Physics News on Phys.org
Cooper Pair

This doesn't talk about the spin, and I didn't even know what a Cooper pair was. So if you're looking for more technical info, I can't help

A condensation effect is also credited with producing superconductivity. In the BCS Theory, pairs of electrons are coupled by lattice interactions, and the pairs (called Cooper pairs) act like bosons and can condense into a state of zero electrical resistance.

The conditions for achieving a Bose-Einstein condensate are quite extreme. The participating particles must be considered to be identical, and this is a condition that is difficult to achieve for whole atoms.
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/spinc.html

I would assume that the spin must also be identical. A little technical help from someone would be nice.

ZapperZ
Staff Emeritus
danitaber said:
Cooper Pair

This doesn't talk about the spin, and I didn't even know what a Cooper pair was. So if you're looking for more technical info, I can't help

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/spinc.html

I would assume that the spin must also be identical. A little technical help from someone would be nice.
I am responding to this thread only because YOU asked, danitaber. This is not a response to the original question of this thread.

In conventional superconductors and superfluids, the "spins" are only relevant to form a composite boson. So the electrons in a pair must form a total net spin that is an integer, i.e. 0, 1, 2, etc... Most conventional Cooper pairs form the singlet spin state, i.e. they pair up antiparallel to each other, resulting in a net spin of 0. But in some superconductors such as the ruthenates, they can form a triplet-spin states , i.e. they pair up parallel to each other forming a net spin of 1. Once they have done that, then they can condense to a BE state and we no longer care about spins.

This isn't true in other exotic systems such as the high-Tc superconductors, because in some scenario, the paring mechanism is magnetic in origin. While they still from singlet pairs, the spins continue to interact with the rest of the material, so one cannot just "forget about it".

If one is so inclined, there have been several different threads on the Cooper Pairs on here that have gone over the very same topic. So looking for those might get one up to speed.

Zz.

ZapperZ, you're so sweet sometimes. :shy:

Thanks, that helped out a lot. (Maybe I should have realized that, but it just didn't get through) but, now that I think about it, that would be the only way a couple of fermions would act like a boson.

And I will take a look at the archive, now.

ZapperZ
Staff Emeritus
danitaber said:
ZapperZ, you're so sweet sometimes. :shy:
You should not say that about me or else DocAl will threaten to give me a warning the same way he's doing to HallsofIvy. :)

Zz.

Looked up Cooper Pairs

Hey, Zz.

There's some neat stuff in the archives. Thanks again. PS Sent you a personal.

Are the spins truly up and down or do they have the same spins (parallel)?

If they are up and down paired, then what causes that orientation?
did this help, what_are_electrons? Helped me.

what_are_electrons
danitaber said:
Hey, Zz.

There's some neat stuff in the archives. Thanks again. PS Sent you a personal.

did this help, what_are_electrons? Helped me.
Yes, ZapperZ's answer helped a lot. Many thanks ZapperZ.

Now, I'd like to know why Pauli's Exclusion Principle, which was defined for an atom NOT a band or a Fermi gas, can be applied to other non-atomic systems? Who decided this and on what basis?

The HyperPhysics site is one of my favorite resources so I already knew about the pairing over a large distance (>100nm), but it did not state that the spins were anti-parallel and that the sum could be integer value. Nor did it state that there are exceptions where the pairs are triplet state. The latter 2 details are news for me. I shall also check this forum's archive for Cooper pair info. Thanks again.

A 3rd detail really has my attention: ie "...as the high-Tc superconductors, because in some scenario, the paring mechanism is magnetic in origin." The pairing is magnetic in origin is especially interesting. Does this mean that all other pairing is due to electric fields or another mechanism? Over what distance is magnetic pairing active? Do magnetically paired electrons form a triplet (spins parallel) or singlet state (spins anti-parallel)?

Staff Emeritus
Gold Member
Dearly Missed
what_are_electrons said:
Yes, ZapperZ's answer helped a lot. Many thanks ZapperZ.

Now, I'd like to know why Pauli's Exclusion Principle, which was defined for an atom NOT a band or a Fermi gas, can be applied to other non-atomic systems? Who decided this and on what basis?
Where did you get the idea that Pauli's exclusion pronciple was defined for an atom? It was originally defined for the electron shells within an atom because that's where the first sign of it turned up, in spectrograms. But it was always about electrons, and photons.

See http://www.arxiv.org/PS_cache/quant-ph/pdf/0403/0403199.pdf [Broken] for a historical account.

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what_are_electrons
Where did you get the idea that Pauli's exclusion pronciple was defined for an atom? It was originally defined for the electron shells within an atom because that's where the first sign of it turned up, in spectrograms. But it was always about electrons, and photons.

See http://www.arxiv.org/PS_cache/quant-ph/pdf/0403/0403199.pdf [Broken] for a historical account.
For some reason I can not access ARXIV.org sites. I'm not at a university maybe. Can not also access xxx.lanl sites.

Some of my references refer to "electron orbits" which are limited to 2 electrons but none to shells which can have up to 32 electrons.

About 50% of my books on atomic physics, quantum physics and related topics, clearly state that PEP applies to either electron orbitals within atoms or multi-electron atoms. The other half do not mention atoms just orbitals or wave functions. Most of the older books include the reference to atoms. It seems that there may be some latitude used with translating the German words Pauli used. I'd love to read the original article in German if you have it.

J.J. Sakurai (1984, 10th printing of Adv. Quantum Mechanics) states "There exists, in nature, particles that do not obey Bose-Einstein statistics but rather obey Fermi-Dirac statistics - electron, muons, protons, etc. We must somehow incorporate the Pauli exclusion principle."

A 2 vol. book titled "The World of the Atom" that is 1800 pages in length and describes in detail much of the details and history of those scientists who efforts directly and indirectly led to the development modern QM and QT. Under the section on W. Pauli, the author of that section wrote:
"Particles such as photons, and certain mesons that are described by symmetrical wave functions, are not governed by this Pauli Exclusion Principle. As Pauli points out in his Nobel address, which follows this commentary, this leads to two types of statistical mechanics to explain the complexity of spectral lines."
This author says photons are not governed by PEP which is the opposite of your writing.

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I really want to know a lot about superconductors, I might even want to work with them when I grow up. But one thing has always puzzled me and I haven't found any place that explain it really well. So can someone explain to me: How exactly do, or should I say, what force keeps the two electrons in a cooper pair from flying apart? I really want to understand this because superconductors, superfulids, BECs and fermonic condensates really facinates me.

what_are_electrons
Entropy said:
I really want to know a lot about superconductors, I might even want to work with them when I grow up. But one thing has always puzzled me and I haven't found any place that explain it really well. So can someone explain to me: How exactly do, or should I say, what force keeps the two electrons in a cooper pair from flying apart? I really want to understand this because superconductors, superfulids, BECs and fermonic condensates really facinates me.
That's an excellent question. Thanks for asking it.

ZapperZ
Staff Emeritus
Entropy said:
I really want to know a lot about superconductors, I might even want to work with them when I grow up. But one thing has always puzzled me and I haven't found any place that explain it really well. So can someone explain to me: How exactly do, or should I say, what force keeps the two electrons in a cooper pair from flying apart? I really want to understand this because superconductors, superfulids, BECs and fermonic condensates really facinates me.
You did not indicate what level of knowledge you have. So don't complain if you can't understand the exact derivation given below.

There are two separate issues that must be understood here: (i) the original Cooper pair problem and (ii) the BCS pairing problem.

(i) shows how, when 2 electrons are placed at an energy just barely above the Fermi level, that even the smallest attractive potential is sufficient to form a bound pair.
http://edu.ioffe.ru/register/?doc=galperin/l18pdf2.tex [Broken]

(ii) extended the Cooper pairing scenario to include ALL of the electrons in the Fermi sea.

Two electrons cannot form bound states when they are by themselves. It requires a lot of other electrons (the Fermi sea) and lattice ions (phonons) to make it possible. This is why this is a many-body effect, or what Laughlin would call an "emergent" phenomena.

These derivations require that you know either variational method or field theoretic/2nd quantization method of QM.

Zz.

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what_are_electrons
ZapperZ said:
.(i) shows how, when 2 electrons are placed at an energy just barely above the Fermi level, that even the smallest attractive potential is sufficient to form a bound pair.
http://edu.ioffe.ru/register/?doc=galperin/l18pdf2.tex [Broken]

(ii) extended the Cooper pairing scenario to include ALL of the electrons in the Fermi sea.

Two electrons cannot form bound states when they are by themselves. It requires a lot of other electrons (the Fermi sea) and lattice ions (phonons) to make it possible. This is why this is a many-body effect, or what Laughlin would call an "emergent" phenomena.
Zz.
Please clarify the nature of the "smallest attractive potential". Is it electric, magnetic or something else?

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The attraction can be from anything! and it doesn't matter how small the force is, it just has to be attractive.

To Entropy's question, hopefully ZZ can chime in here. This is something me and my advisor have debated. The cooper pairs lifetime is infinite, you can break a pair and form quasiparticles by exciting the system. But the reason they form is that the bound state have a lower energy than the normal state.

JMD

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ZapperZ
Staff Emeritus
nbo10 said:
To Entropy's question, hopefully ZZ can chime in here. This is something me and my advisor have debated. The cooper pairs lifetime is infinite, you can break a pair and form quasiparticles by exciting the system. But the reason they form is that the bound state have a lower energy than the normal state.

JMD
I could have "chimed in" a lot sooner than this, but each time I formulated something to say, I started thinking of all the exceptions to the "rule" and gave up. So I will state the caveat to what I will say below by stating that this is the "naive" version as applied to conventional superconductors (but with some examples taken from high-Tc superconductors).

While it is somewhat true that below Tc, the Cooper pairs have an "infinite" lifetime, we need to be careful on what we mean here. It is true that if you fix the temperature to a value below Tc, the SUPERFLUID DENSITY remains constant at an equilibrium value. It means that the density of Cooper pairs remains constant. However, it doesn'tmean that each Cooper pair remains in the same state forever. This is due to two factors:

(1) the indistinguishibility of each Cooper pair. You can't tag one Cooper pair and follow it around. Remember, these are bosons, and when you say that, it implies the indistinguishibility of quantum statistics has already kicked in. So we can't say that THAT particular cooper pair has an infinite lifetime, because you don't have the ability to pick out a cooper pair.

(2) In the BCS formulation, there is nothing preventing one cooper pair being scattered out of a particular (k1_up, -k1_down) state, and 2 electrons from the Fermi sea coming in and taking over. In other words, it is perfectly "legal" for a continuous scattering in and out of Cooper pair states. All it requires is that at a fix T, the density of cooper pairs reaches an equilibrium.

Now, the quasiparticles are a different matter completely. Let me first say that there is a HUGE amount of background info that one needs to understand what a "quasiparticle" is. The relevant information is contained within Landau's Fermi Liquid theory. In a superconductor, the quasiparticle is a single-particle excitation in the NORMAL state, i.e. not in a condensed Cooper pair. In fact, to be exact, the quasiparticles are the ones that form the Cooper pairs, not the bare electrons or holes.

In a conventional superconductor, when you break a cooper pair, you form two quasiparticles. This is because the normal state of a conventional superconductor can be accurately described as a Fermi liquid. Unfortunately, this breaks down in high-Tc superconductors, especially in the optimally doped and underdoped regime. The normal state of these materials have no "well-defined" quasiparticles. This then is the impetus for many theoriests to argue that conventional BCS theory will not work for high-Tc superconductors because the material we are studying starts off as being "strange", i.e. non-Fermi Liquid.

Now, this would fine and dandy, except the damn thing throws us another curve. The ARPES spectra in my avatar is from a highly overdoped Bi2212 high-Tc material (Tc ~ 51K). We found that while the underdoped and optimally doped compounds behave in a non-Fermi Liquid manner, the overdoped ones start to show Fermi Liquid-like characteristics! It starts to show well-defined quasiparticle in the normal state. If all these observations are true, then we have to reconcile the fact that this thing has two wildly different characteristics. We have to figure out if the boundary between these two are simply a gradual crossover, or a distinct phase transition.

I hope this illustrates my claim in another thread on why we should not delve into high-Tc materials or else we'll go mad! :)

Zz. [who got out of studying high-Tc superconductors 3 years ago]

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ZapperZ:
I hope this illustrates my claim in another thread on why we should not delve into high-Tc materials or else we'll go mad! :)

Kurious:
Do you think there will ever be a theory that will
predict and describe all possible superconductor behaviour?