BCS Theory: Noobish Question Explained

[jostpuur]

I tried to get a grasp on BCS theory by reading the Wikipedia article http://en.wikipedia.org/wiki/BCS_theory. It says

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density. The two electrons are then held together with a certain binding energy. If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

I understand the part where the bound electron pair can resist from being torn apart by kicks from thermal oscillations, but what I did not understand is that why does the pair as whole not get scattered by the kicks?

 

[ZapperZ]

If there ever is an example on why one should not use Wikipedia, this would be it.

Zz.

 

[will.c]

If there ever is an example on why one should not use Wikipedia, this would be it.

Zz.

?!

Please elaborate. I don't know much about BCS theory, but I don't see why an incomplete article is an indictment of the format as a whole. If you can answer jostpuur's question, please do. You could, yourself, then clarify what you disagree with in the Wikipedia description on Wikipedia itself. This would improve the experience of all users of Wikipedia, which, despite your feelings is a popular starting point for many people looking for introductory information on scientific topics (an area in which it tends to be quite accurate, again, if incomplete).

To jostpuur, the Wikipedia article also links to the hyperphysics article on BCS (http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bcs.html). Maybe this source will resolve your problem.

 

[ZapperZ]

?!

Please elaborate. I don't know much about BCS theory, but I don't see why an incomplete article is an indictment of the format as a whole. If you can answer jostpuur's question, please do. You could, yourself, then clarify what you disagree with in the Wikipedia description on Wikipedia itself. This would improve the experience of all users of Wikipedia, which, despite your feelings is a popular starting point for many people looking for introductory information on scientific topics (an area in which it tends to be quite accurate, again, if incomplete).

Fine. Let's look at it carefully, shall we?

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density.

1. What's the relevance of the "spin" here? It didn't say. Someone reading this would naturally want to ask why would it matter that it will only attract another electron of the opposite spin, since all we are dealing with in that quote is electrostatic interaction of electrons with the positive ions. So why would spin matter?

2. In fact, we CAN have bound states with electron with the SAME spin orientation, resulting in spin-triplet superconductors.

The two electrons are then held together with a certain binding energy.

This is not quite right IF one is dealing with the cartoon picture above that has been given. The electron is moving extremely fast when compared to the ion movement, resulting in the lattice deformation. By the time the lattice is at its maximum deformation (and thus, most "attractive" to another electron), that first electron has been long gone. These two electrons are really not "held together" in such a sense within that cartoon picture. It can't be.

If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

This is the kicker of them all (pun intended). The "oscillating atoms" (this is not correct because they are actually oscillating lattice IONS), or technically the phonons of the system, IS the glue of a BCS superconductor. However, these "glue" is actually a virtual exchange of interaction between the two electrons. The binding energy IS a function of the "kicks" (strange analogy), not in spite of it.

I will say it again. Wikipedia may have bits and pieces of it sounding right, but pedagogically, it is horrendously difficult to follow. When one mixes metaphors like what is happening here, one end up with contradicting scenarios.

Zz.

 

[will.c]

Thank you!

You've clarified the picture, which, as the article stands would produce completely incorrect physics, and while jostpuur's question remains unanswered (here) at least the answer would follow from the picture you provided. I say without a hint of sarcasm that that post has made the world a better place.

The next step would be editing the article to reflect this. No one expects it to be a textbook, but that's again no reason to write it off entirely. I know I can't afford to purchase a book on BCS right now, and A quick google search isn't bringing up anything both satisfying and at an introductory level (one could of course, argue that this is natural. There's little point in a guide to theories of superconductivity for nonscientists) but if the Wikipedia article was close enough in the first place it would be ideal - like it or not, people are going to continue to go there en masse, and I think it's more proper to correct Wikipedia than to correct people individually (by telling them only that Wikipedia mislead them, until pressed further)

 

[ZapperZ]

Thank you!

You've clarified the picture, which, as the article stands would produce completely incorrect physics, and while jostpuur's question remains unanswered (here) at least the answer would follow from the picture you provided. I say without a hint of sarcasm that that post has made the world a better place.

The next step would be editing the article to reflect this. No one expects it to be a textbook, but that's again no reason to write it off entirely. I know I can't afford to purchase a book on BCS right now, and A quick google search isn't bringing up anything both satisfying and at an introductory level (one could of course, argue that this is natural. There's little point in a guide to theories of superconductivity for nonscientists) but if the Wikipedia article was close enough in the first place it would be ideal - like it or not, people are going to continue to go there en masse, and I think it's more proper to correct Wikipedia than to correct people individually (by telling them only that Wikipedia mislead them, until pressed further)

But see, you are missing the point altogether.

Being "pedagogically unsound" is a criticism of the PHILOSOPHY of wikipedia. The reason why textbooks writers spend years figuring out what to write has nothing to do what to cover, but HOW to cover the material It takes a lot of effort and thought to present things in a systematic, clear manner, i.e pedagogically sound. Wikipedia can't do that, especially when you have so many people sticking their hands into various part of the same entry, AND editing what each other has written. I am not going to waste my time correcting something only to be "corrected" later, either on the content, or on how I presented it. The flaw is in the philosophy of the system, something that I refuse to be a part of.

It isn't JUST about content. It is also about how it is presented. Any book writer putting his or her name on it will care about both. It is why we have our favorite textbooks, even when all of them cover the same material. It is because some are clearer than others at presenting the same material. This is what most people forget.

Zz.

 

[f95toli]

The main problem here is that it is probably impossible to give a "simple" explanation of BCS theory, even though it is not a very complicated theory compared to most other problems in many-particle physics it is still post-grad level physics. Perhaps you can learn about some of of the basic ideas (Cooper pairs, overscreening, electron-phonon interaction etc) but in order to really understand the theory you need to work through- and understand all the relevant math.
I.e. I don't think you can understand it from reading an article of two in wikipedia or any other on-line resource.

 

[jostpuur]

Ok. This was not serious. I was merely spending my time reading Wikipedia (and thinking a little bit at the same time).

It could I'm taking a course on many-body physics in the fall.

 

[Minich]

BCS does not explain Superfluidity of electron gas :(((

I understand the part where the bound electron pair can resist from being torn apart by kicks from thermal oscillations, but what I did not understand is that why does the pair as whole not get scattered by the kicks?

Never mind! In 1973 i took an exam in Quantum Field theory and told the examiner that BCS-Gorkov theory does not explain the SUPERFLUIDITY of electron gas in superconductors. The examiner (Professor of Physics) was rather in embarassment, but after some conversation was have to admit that he also don't have any correct proof, that electron gas in superconductors MUST be superfluid.

And nobody among my studentfriends of our famous Department of Quantum Mechanics couldn't explain this phenomenon, when i asked them ))

By the way I've got very good mark for that exam.

I was not the only person who thinks that BCS theory does not explain SUPERFLUID properties of electron gas and Meissner effect in superconductors.

So did Leon Niels Cooper (the author of "Cooper pairing" and BCS) think. As everybody knows BCS theory was published in 1957. In 1959 Cooper published review paper "Theory of superconductivity". There he wrote that BCS theory itself does not explain superfluidity of electron gas and Meissner effect.
See the original:
"Adv. Phys. 8, number 29, 1-44, 1959"
I can't give the scan (quotes) of this work in english, i have this paper only in russian translation of 1960.

So there is a question "Who invented the rumor, that BCS is the theory of SUPERFLUID electron gas?"
Or "Who and when proved rigorously (theoretically), that electron gas in superconductors MUST be superfluid?"


Who disagree, do not, please, discuss secondary properties of superconductors (type of phase transition, thermal properties, gaps of all types, flux quantization, usual and unusual isotopic effects and so on).

If anybody knows clear and obvious theoretical proof of superfluidity of electron gas it should be the tremendous achivement )

 

[ZapperZ]

Er.. you do know that after Deborah Jin's recent experiment on fermion condensate, that we now know that the BEC-BCS connection is a smooth crossover rather than a transition, don't you? It shows that one can go from BEC to BCS and vice versa.

Zz.

 

[Minich]

I tried to answer the main question of this thread:

why does the pair as whole not get scattered by the kicks?

And this question is not connected with experiment: we all know that experimentally superconductivity exist!

But rephrasing topicstarter question: why so called "Cooper pair"s scatter such a way, that there can exist persistent current? Can we see the CALCULATIONs? Who can calculate the lifetime of persistent current, it's stability to external forces (rotation acelleration, changing the shape of superconductor wire,,,,).

I don't see anybody who gave appropriate answer in this thread. Who can give professional answer?

 

[ZapperZ]

I tried to answer the main question of this thread:


And this question is not connected with experiment: we all know that experimentally superconductivity exist!

But rephrasing topicstarter question: why so called "Cooper pair"s scatter such a way, that there can exist persistent current? Can we see the CALCULATIONs? Who can calculate the lifetime of persistent current, it's stability to external forces (rotation acelleration, changing the shape of superconductor wire,,,,).

I don't see anybody who gave appropriate answer in this thread. Who can give professional answer?

This is very strange. It is like you are asking why plane waves as wavefunctions in QM are non-local! That is basically the BCS ground state!

Zz.