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Mk

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What is the BCS theory?
 

Njorl

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Isn't it the formula the NCAA uses to determine who will be in the high-profile college football bowl games. Evidently, the uncertainty principle applies to it in a macroscopically noticeable way.

Njorl
 

Mk

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It is the theory on how superconductors work but I don't know much else. Cooper Pairs, crystal latice?
 
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While it isn't a full-fledged answer to elucidate the nature of the theory, this article does give a pretty succint description of the affairs:

http://www.nobel.se/physics/laureates/2003/public.html [Broken]
http://www.nobel.se/physics/laureates/2003/phyadv03.pdf [Broken] (a more advanced version of the article, comprised of various equations).
http://www.physics.carleton.ca/courses/75.364/mp-2html/node16.html#SECTION00017000000000000000 [Broken]

Almost 50 years passed before the physicists John Bardeen, Leon Cooper and Robert Schrieffer (Nobel Prize in Physics, 1972) were able to present a theory (the BCS theory, named after the initials of their surnames) that explained the phenomenon. This theory shows that some of the negatively-charged electrons in a superconductor form pairs, called Cooper pairs. These pairs of electrons flow along attracting channels formed by the regular structure of the positively-charged metal atoms in the material. As a result of this combination and interaction the current can flow evenly and superconductivity occurs. The paired electrons are usually thought of as a condensate, similar to the drops of liquid that form in a cooled gas. Unlike an ordinary liquid this “electronic liquid” is superconductive.

These superconductors are called type-I. They are metals and are characterised by the Meissner effect, that is, in the superconductive state they actively counteract a surrounding magnetic field as long as its strength does not exceed a certain limit (fig. 1). If the surrounding magnetic field becomes too strong, the superconductive property disappears.

But it is known that there are superconductors that lack or show only a partial Meissner effect. These are in general alloys of various metals or compounds consisting of non-metals and copper. These retain their superconductive property even in a strong magnetic field. Experiments show that the properties of these so-called type-II superconductors cannot be described by the BCS theory.
 
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So what's actually the most accepted theory to explain superconductivity? RVB theory?
 
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Originally posted by meteor
So what's actually the most accepted theory to explain superconductivity? RVB theory?
Yep, it seems the resonating valence bond (RVB) theory is indeed the most acceptable theory we have at our disposal.

As the article itself explicitly apprise:
The theory Abrikosov's argument was based on was formulated in the early 1950s by Vitaly Ginzburg and Lev Landau (the latter was awarded the Nobel Prize in Physics in 1962 for other work, see below). This theory was intended to describe superconductivity and critical magnetic field strengths in the superconductors that were known at that time. Ginzburg and Landau realised that an order parameter (wave function) describing the density of the superconductive condensate in the material had to be introduced if the interaction between the superconductor and magnetism was to be explained. When this parameter was introduced, it was evident that there was a breakpoint when a characteristic value approximately 0.71 was reached and that in principle there were two types of superconductor. For mercury the value is approximately 0.16 and other superconductors known at the time have values close to this. There was therefore, at that time, no reason to consider values above the breakpoint. Abrikosov was able to tie up the theory by showing that type-II superconductors had precisely these values.
 
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I seem to remember Brian Green also talking about a BCS theory in his Elegant Universe. It was a theory allowing predictions on the shape of the Calabi-Yau manifolds and I think it's related to this one in superconductivity and he was also calling it Beyond C(I don't remember) States.
 
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Is possible that Green was talking about BPS states? I know that BPS states appear in string theory, but I'm not aware of any connection between BCS theory and string theory
 
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Originally posted by meteor
Is possible that Green was talking about BPS states? I know that BPS states appear in string theory, but I'm not aware of any connection between BCS theory and string theory
sorry, they sound the same, i have no idea about any of them so... I should have remembered that second word. what does BPS come from?
 
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BPS comes from Bogomolny-Prasad-Sommerfield, three physicists. In superstring theory, BPS states are solitons. D-branes, p-branes and extremal black holes are examples of BPS states in superstring theory
 
So soliton theory plays an important role in String/M-theory? That's nice to know, because at the theoretical physics department at my university, they mainly focus on String and soliton theory...
 
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Originally posted by Dimitri Terryn
So soliton theory plays an important role in String/M-theory? That's nice to know, because at the theoretical physics department at my university, they mainly focus on String and soliton theory...
Soliton theory is a major driving force behind the latest advances in Superstring/M-Theory, especially nowdays. It's the prima field of research, so yeah, i guess it's pretty important :)
 

ZapperZ

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re: RVB theory. I do not believe it is considered as the most widely accepted theory, at least not for the high-Tc superconductors. In fact, there are a number of experimental evidence that appears to contradict RVB predictions. The current champion of RVB theory is Phil Anderson of Princeton. A preprint by him appeared recently in the e-print archive at

http://arxiv.org/abs/cond-mat/0311467

However, it didn't take long for dissenting views of this to appear. See

http://arxiv.org/abs/cond-mat/0312385

I have attended many conferences in which RVB scenario isn't "widely accepted". There are still major problems with it.

re: BCS Theory. It is incorrect to say that BCS theory doesn't work for Type II conventional superconductors. The work of Abrikosov was on just that, the extension of BCS theory to account for these material. In fact, the BCS theory is so powerful that Tony Leggett was able to show that it also can be extended to not only superfluid He4, but also to He3. Both Abrikosov and Leggett, along with Vitaly Ginzburg won the 2003 Physics Nobel prize.

Zz.
 
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Originally posted by ZapperZ
re: RVB theory. I do not believe it is considered as the most widely accepted theory, at least not for the high-Tc superconductors. In fact, there are a number of experimental evidence that appears to contradict RVB predictions. The current champion of RVB theory is Phil Anderson of Princeton. A preprint by him appeared recently in the e-print archive at

http://arxiv.org/abs/cond-mat/0311467

However, it didn't take long for dissenting views of this to appear. See

http://arxiv.org/abs/cond-mat/0312385

I have attended many conferences in which RVB scenario isn't "widely accepted". There are still major problems with it.

re: BCS Theory. It is incorrect to say that BCS theory doesn't work for Type II conventional superconductors. The work of Abrikosov was on just that, the extension of BCS theory to account for these material. In fact, the BCS theory is so powerful that Tony Leggett was able to show that it also can be extended to not only superfluid He4, but also to He3. Both Abrikosov and Leggett, along with Vitaly Ginzburg won the 2003 Physics Nobel prize.

Zz.

BCS theory states that Superconductivity occurs through the formation of "Cooper" pairs: At low temperature, electrons starts to attract each other via lattice vibration (phonons) and form pairs, i.e. electron orbits around each other. Now, the "speed" of rotation of one pair is characterized by a number: L=0 (s-wave superconductors), L=1 (p-wave superconductors), L=2 (d-wave superconductor), etc...

The BCS theory works perfectly well for so-called "conventional" superconductors which are S-wave type (L=0) and which can be Type-I OR type-II superconductors.

The difference between type-I and type-II supercondcutors is given by their response to an external magnetic field: A type-I superconductor does NOT let any external magnetic field penetrates its body while a type-II superconductor can PARTIALLY let a external magnetic field penetrates its body.

Now, high-Tc superconductors (which experimentally occur to be of type-II as far as their magnetic properties are concerned) seem not to be "conventional" superconductors. Their pairing seems to be of the p-wave or d-wave type. This is still included in the BCS theory.

However, there are theoretical difficulties (in High-Tc superconductors) to determine the nature of the interaction which induces the paring of electrons: It may be that the lattice vibrations are not the right candidate for High-Tc superconductors. And the RVB model is an alternative to the BCS model. Further experimental work is required to the conclude that debate...

NOW, the superfluidity of Helium-4 has nothing to do with the BCS theory. The superfluidity of Helium-4 (at 2 Kelvin) is due to a BOSE-EINSTEIN condensation (BEC),

AND the BCS theory is not EXTENDED, but strictly APPLIES to superfluid Helium-3 (at 2 millikelvin). Simply the interaction leading to the pairing of helium-3 atoms is magnetic in nature and is not due to lattice vibrations which do NOT exist in liquids. Note that the pairing in superfluid helium-3 is a p-wave type (L=1).
 

ZapperZ

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Originally posted by roch
BCS theory states that Superconductivity occurs through the formation of "Cooper" pairs: At low temperature, electrons starts to attract each other via lattice vibration (phonons) and form pairs, i.e. electron orbits around each other. Now, the "speed" of rotation of one pair is characterized by a number: L=0 (s-wave superconductors), L=1 (p-wave superconductors), L=2 (d-wave superconductor), etc...

The BCS theory works perfectly well for so-called "conventional" superconductors which are S-wave type (L=0) and which can be Type-I OR type-II superconductors.

The difference between type-I and type-II supercondcutors is given by their response to an external magnetic field: A type-I superconductor does NOT let any external magnetic field penetrates its body while a type-II superconductor can PARTIALLY let a external magnetic field penetrates its body.
Correct. That's what I was responding to when I pointed out that it is not correct to say that BCS theory doesn't work for all Type II superconductors. I should have clarified that this does NOT include high-Tc superconductors.

[/i]
Now, high-Tc superconductors (which experimentally occur to be of type-II as far as their magnetic properties are concerned) seem not to be "conventional" superconductors. Their pairing seems to be of the p-wave or d-wave type. This is still included in the BCS theory.

However, there are theoretical difficulties (in High-Tc superconductors) to determine the nature of the interaction which induces the paring of electrons: It may be that the lattice vibrations are not the right candidate for High-Tc superconductors. And the RVB model is an alternative to the BCS model. Further experimental work is required to the conclude that debate...
[/QUOTE]

I'm not disputing that RVB theory is an alternative. I am disputing that it is "widely accepted". Nothing that I have seen so far would indicate that the community are moving in this direction.

[/i]
NOW, the superfluidity of Helium-4 has nothing to do with the BCS theory. The superfluidity of Helium-4 (at 2 Kelvin) is due to a BOSE-EINSTEIN condensation (BEC),

AND the BCS theory is not EXTENDED, but strictly APPLIES to superfluid Helium-3 (at 2 millikelvin). Simply the interaction leading to the pairing of helium-3 atoms is magnetic in nature and is not due to lattice vibrations which do NOT exist in liquids. Note that the pairing in superfluid helium-3 is a p-wave type (L=1).
[/QUOTE]

You are correct. I was being sloppy at using what I term as "BCS" theory. I included the cooper pairing as part of it. However, BCS theory in itself is independent of the "glue" that causes this pairing. While the BCS paper of 1957 did use phonons as the mechanism, the fundamental theory itself is adaptable to any kind of mechanism. So even if spin fluctuations end up being the paring mechanism, that is perfectly acceptable within the BCS model. That's why I pointed out the He3 case (He4 example was the brain-dead part of my posting just now). Incidentally, I believe the ruthenates also have p-wave symmetry AND where BCS theory have more successes than for the cuprates.

Zz.
 
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Originally posted by ZapperZ

I'm not disputing that RVB theory is an alternative. I am disputing that it is "widely accepted". Nothing that I have seen so far would indicate that the community are moving in this direction.
[/i]
Zz.
I agree on that point, i.e. it is far from being "widely accepted".

I would like to mention that it is always very useful to give references to publications (as you did in your former post). That should be more of an habit in these forum. That helps to clarify what we are talking about.
 

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