Please explain the BCS theory. (1 Viewer)

[jules.09]

Please clearly and logically explain the BCS theory.

I don't see how the lattice can warp, it makes sense in the isolated case (in a textbook schematic diagram) but you're told that the electrons move collectively and coherently through the lattice, and these cooper pairs somehow just break up and reform. And it is apparently an exception to the Pauli exclusion principle.

Which doesn't help.

Any help would be most appreciated.

 

[gabgab]

Okay, here goes haha.

Basically, the textbooks are wrong. wrong wrong wrong hahaha.

Our teacher went to a lecture thing on it.

The "cooper pairs" theory, and the diagram that goes with it, hasn't been updated since it was first proposed by Bardeen, Cooper, and Shcrieffer. (or however you spell it).

The cooper pairs are not actually "pairs" as such. They do not have to be next to each other or moving in the same direction to be a cooper pair, that was just the basic model they proposed so that average people could grasp the concept.

One electron travels through the lattice, and because the lattice is positively charged, and the electron negative, the lattice distorts. Then, another electron from anywhere else in the structure is attracted to the positive area created by the lattice distortion.

But, it isnt necessary to like, learn that bit. Just study the diagram, and even though it doesnt make sense, the syllabus doesn't specify as to whether it wants the correct version or not, so just use the one out fo your textbook, cuz some old wrinkly HSC marker might not know the real theory, and might think your on drugs or something.

sigh.

 

[Shanku]

Please clearly and logically explain the BCS theory.

I don't see how the lattice can warp, it makes sense in the isolated case (in a textbook schematic diagram) but you're told that the electrons move collectively and coherently through the lattice, and these cooper pairs somehow just break up and reform. And it is apparently an exception to the Pauli exclusion principle.

Which doesn't help.

Any help would be most appreciated.

BCS Theory basically explains how Cooper pairs form within the lattice structure of a certain material.

The first thing you need to know (which a lot of people forget to take into consideration when trying to understand BCS Theory) is that electrons are WAY smaller and lighter than the positive ions in the lattice structure (I think an electron is nearly 1/2000th the mass of a positive ion).

The positive ions are basically at the "corners" of the lattice structures and can move around a bit, but generally stay in the same spot (because positive ions repel each other and hence distance themselves accordingly). When an electron zooms through the structure, the positive ions get attracted to the negative electrons (if you forgot that like charges repel and unlike charges attract then you're in serious trouble for the HSC).

Since the positive ions are fat shits, they heave their fat asses towards where they think the sexy electron is, which takes a while. However, the electron is pretty fast (and she's playing hard to get) so by the time the positive ion gets to where it thought the electron was, the electron has already propagated further through the lattice. Since the electron is travelling through the lattice, it sets off a "mexican wave" of those fat ass positive ions towards where they think the electron is. This is in 3D so the positive ions are potentially coming from all angles. Thus, a concentration of positively charged particles exist in this area. Another electron "sees" this concentration, and being the cougar that she is, she zooms towards it. This makes it look like that electron is "paired up" with the previous electron because they're pretty close to each other compared to the distance between other electrons.

This electron actually comes from the OPPOSITE direction to the first one (because momentum must be conserved). Also, the distance between these electrons can be hundreds and thousands of ions apart. This distance is known as the coherence length. In most textbooks, it is shown to be only a few ions apart for illustrative purposes.

I hope this helps.

Cheers,
Shanku

 

[Dumbledore]

i don't get this about BCS theory

BCS theory is supposed to explain how superconductivty works - how current can flow though the lattice without resistance.
it is known that electrical resistance is caused by collisions between the electrons and the lattice. all these text books and notes go on about how electrons use charge to distort the lattice, exchange phonons of energy, creating positively charged areas that attracts other electrons to form cooper pairs, what does this prove? in the end it explains nothing about the reason why electrons do not collide with the lattice at temperatures below the critical temperature and hence it doesn't explain how superconductivity works.

ok i might have missed it, but i read notes from BOS, my textbook, sites and i still don't get this part

 

[jules.09]

This is in 3D so the positive ions are potentially coming from all angles. Thus, a concentration of positively charged particles exist in this area. Another electron "sees" this concentration, and being the cougar that she is, she zooms towards it.
...

Also, the distance between these electrons can be hundreds and thousands of ions apart.

I agree with most of what you've written, but like Dumbledore said in the previous post, I don't see how this explains superconductivity, really.

You've outlined an isolated case, but aren't there many "concentrations of positively charged particles" throughout the lattice? Because every electron should be effectively causing these areas, and chasing after another electron, which really, seems pretty chaotic. It doesn't really sound like a cooper pair, as it does a whole chain..

In this respect, how does it differ from a normal conductor rtp?

And must the coherence length be that far apart? I mean, yes, it can be hundreds and thousands of ions apart, but what if it is much closer?

This is so quirky.

Thanks anyway; suppose you could iron out those creases?

 

[darkchild69]

According to the BCS theory, when a superconductor is cooled to below the critical temperature, the very low thermal energy leads to a quantum state where an electron can lead to a distortion in the lattice of positive nuclei to give rise to a localized positive region, which attracts a second electron in to combine with the first as a “cooper pair”. The “Cooper pair” then seems to be able to interact with the lattice nuclei, resulting in no destructive interference, and it is able to move through the lattice with no loss of energy.
Based on the very low thermal energy giving rise to a quantum state where the first electron can distort the lattice, resulting in a second electron falling in to form the Cooper pair, the BCS theory is able to explain how, through the exchange of phonons and the slight lattice distortions, a superconductor below the critical temperature has zero resistance to flow of electric current

i don't get this about BCS theory

BCS theory is supposed to explain how superconductivty works - how current can flow though the lattice without resistance.
it is known that electrical resistance is caused by collisions between the electrons and the lattice. all these text books and notes go on about how electrons use charge to distort the lattice, exchange phonons of energy, creating positively charged areas that attracts other electrons to form cooper pairs, what does this prove? in the end it explains nothing about the reason why electrons do not collide with the lattice at temperatures below the critical temperature and hence it doesn't explain how superconductivity works.

ok i might have missed it, but i read notes from BOS, my textbook, sites and i still don't get this part

I'll try to expand on this point for you.

The interaction between a Cooper Pair is transient. Each electron in the pair goes on to from a Cooper pair with other electrons, and this process continues with the newly formed Cooper pair so that each electron goes on to form a Cooper pair with other electrons. The end result is that each electron in the solid is attracted to every other electron forming a large network of interactions. Causing just one of these electrons to collide and scatter from atoms in the lattice means the whole network of electrons must be made to collide, which is energeticlly too costly. The collective behaviour of all the electrons in the solid prevents any further collisions with the lattice. Nature prefers situations that spend a minimum of energy and in this case, the minimum energy situation is to have no collisions take place.

BCS theory is actually quantum mechanical. The electrons are described by a wave function that extends throughout the solid and overlaps with other electron wave functions. As a result, the whole network of electrons behaves like one wave function so that their collective moment is coherent.

Another requirement of the BCS theory is that the spins of the Cooper Pair electrons be in opposite directions.

For the High Critical Temp superconductors, their coherence length can actually be as small as one or two atomic spacings and as such it is generally accepted that the Cooper Pairs are not due to lattice deformations but associated with the antiferromagnetism of the Copper Oxide Layers!

That is why BCS theory cannot explain high temp superconductors!

 

[jules.09]

According to the BCS theory, when a superconductor is cooled to below the critical temperature, the very low thermal energy leads to a quantum state where an electron can lead to a distortion in the lattice of positive nuclei to give rise to a localized positive region, which attracts a second electron in to combine with the first as a “cooper pair”. The “Cooper pair” then seems to be able to interact with the lattice nuclei, resulting in no destructive interference, and it is able to move through the lattice with no loss of energy.
Based on the very low thermal energy giving rise to a quantum state where the first electron can distort the lattice, resulting in a second electron falling in to form the Cooper pair, the BCS theory is able to explain how, through the exchange of phonons and the slight lattice distortions, a superconductor below the critical temperature has zero resistance to flow of electric current

Okay, very coherent. Is this actually true? I find it difficult to understand how this works.

 

[darkchild69]

Okay, very coherent. Is this actually true? I find it difficult to understand how this works.

In order to correctly describe BCS theory, you need to delve into wave functions (i.e., quantum physics)

What is needed to be known for full marks in the HSC is over simplified and some is actually incorrect.

All that needs to be said to get full marks would be:
- Electron travels through the lattice
- Loss of energy is typically due to interaction between electrons and impurities or vibration of crystal lattice
- At lower than critical temp, the lattice does not vibrate
- As electrons move through lattice, positive atoms attracted to negative electrons and hence move towards the electron creating a slightly more dense positive region
- This region then attracts a second electron and acts as a "Cooper Pair"
- This "Cooper Pair" then travel through the lattice unimpeded

 

[jules.09]

In order to correctly describe BCS theory, you need to delve into wave functions (i.e., quantum physics)

What is needed to be known for full marks in the HSC is over simplified and some is actually incorrect.

All that needs to be said to get full marks would be:
- Electron travels through the lattice
- Loss of energy is typically due to interaction between electrons and impurities or vibration of crystal lattice
- At lower than critical temp, the lattice does not vibrate
- As electrons move through lattice, positive atoms attracted to negative electrons and hence move towards the electron creating a slightly more dense positive region
- This region then attracts a second electron and acts as a "Cooper Pair"
- This "Cooper Pair" then travel through the lattice unimpeded

I thought the vibration was minimised, but zilch vibration occurs at absolute zero, which has yet to be achieved; that's strange.
I thought the vibration was required to produce the phonons, which create that slipstream effect too?

But I like this simplification. Thank you very much.

 

[darkchild69]

Well, really it's the vibrations (phonons) which cause the superconductivity! But "effectively" the lattice has stopped vibrating, except for these phonons.. Which are really happening everywhere, all the time! (AAAARGGGGGGGGGGGGGGHHH! This is why i hate simplified Physics!)

This reminds me of when i was teaching Bohr's contribution to black body radiation and a student asked, how does this show that. I said "It doesn't, but it's what you need to know to get full marks.."

I then went on to explain and derive the equation which Bohr actually used to describe the curve, and in the denominator you see the familiar hc/lambda, Using the Wein Displacement Law and some other equation i forget the name of, then i told them.. THIS IS WHAT REALLY HAPPENS, NOW JUST FUCKING FORGET IT AND LETS DO THIS LA DI DA BULLSHIT FIZZZICKS

Slipstream effect just refers to the electrons following eachother, which really does not happen either! AAAAAAAAAAAAAAAAAAAAAAAAAARRRRRRRRRRRRRRGH!

 

[jules.09]

Well, really it's the vibrations (phonons) which cause the superconductivity! But "effectively" the lattice has stopped vibrating, except for these phonons.. Which are really happening everywhere, all the time! (AAAARGGGGGGGGGGGGGGHHH! This is why i hate simplified Physics!)

This reminds me of when i was teaching Bohr's contribution to black body radiation and a student asked, how does this show that. I said "It doesn't, but it's what you need to know to get full marks.."

I then went on to explain and derive the equation which Bohr actually used to describe the curve, and in the denominator you see the familiar hc/lambda, Using the Wein Displacement Law and some other equation i forget the name of, then i told them.. THIS IS WHAT REALLY HAPPENS, NOW JUST FUCKING FORGET IT AND LETS DO THIS LA DI DA BULLSHIT FIZZZICKS

Slipstream effect just refers to the electrons following eachother, which really does not happen either! AAAAAAAAAAAAAAAAAAAAAAAAAARRRRRRRRRRRRRRGH!

Yes, it was to be suspected.

I am now utterly confused and equally, amused.

 

[eriito]

I like Shanku's explanation

 

[youngminii]

Shanku's explanation is pretty much right, except he forgot the phonons.. The second electron reaches the first electron but cannot 'pair up' because of basic electrostatic forces (like charges repel). However, the lattice distortions (positive ions trying to reach the electrons) that were created by the first electron 'causes the lattice to release phonons which are absorbed by the second electron, giving it enough energy to overcome the repulsion and pair up with the first electron.
Remember that cooper pairs don't act like electrons, they have completely different properties. Anyway, as they move along the lattice, they repel the lattice as they move along allowing them to travel through unhindered (and since electrons are the charge carriers, there is no resistance). The phonons that are released due to these lattice distortions are absorbed by the cooper pair, giving it enough energy to keep moving.

What's important to note is that resistance in a material is just when electrons try and travel through the lattice, but since it's vibrating so much the electrons keep hitting the lattice structure and end up bouncing everywhere (randomly) until it finally goes back on track. The BCS theory says that the cooper pairs repel the lattice, hence no resistance.

 

[random-1005]

Please clearly and logically explain the BCS theory.

I don't see how the lattice can warp, it makes sense in the isolated case (in a textbook schematic diagram) but you're told that the electrons move collectively and coherently through the lattice, and these cooper pairs somehow just break up and reform. And it is apparently an exception to the Pauli exclusion principle.

Which doesn't help.

Any help would be most appreciated.

the BCS theory is soo easy, how can you not get it, the whole ideas module is the easiest section of the course, its just like yr11 chemistry and a light revision of motors and generators with like a few extra concepts, nothing hard

 

[jules.09]

Shanku's explanation is pretty much right, except he forgot the phonons.. The second electron reaches the first electron but cannot 'pair up' because of basic electrostatic forces (like charges repel). However, the lattice distortions (positive ions trying to reach the electrons) that were created by the first electron 'causes the lattice to release phonons which are absorbed by the second electron, giving it enough energy to overcome the repulsion and pair up with the first electron.
Remember that cooper pairs don't act like electrons, they have completely different properties. Anyway, as they move along the lattice, they repel the lattice as they move along allowing them to travel through unhindered (and since electrons are the charge carriers, there is no resistance). The phonons that are released due to these lattice distortions are absorbed by the cooper pair, giving it enough energy to keep moving.

What's important to note is that resistance in a material is just when electrons try and travel through the lattice, but since it's vibrating so much the electrons keep hitting the lattice structure and end up bouncing everywhere (randomly) until it finally goes back on track. The BCS theory says that the cooper pairs repel the lattice, hence no resistance.

Pretty clear, but the phonons ARE the crystal lattice vibrations. So I don't think it's the "phonons that are released due to these lattice distortions".

The 1st cooper e- that moves through deforms part of the lattice electrostatically (positive/negative attraction).
The 2nd cooper e- is attracted to the net positive charge of the deformation.

This occurs in the opposite direction, to conserve momentum.

The cooper pairs are transient as darkchild69 said. They move on to interact with other e- present in the lattice, cooper pairing with them. If an e- collides with the lattice, this will disrupt the whole network of e-. Nature is a lazy bastard, so it wants to expend as little energy as possible. Therefore there will be no e- colliding with the lattice, and hence, superconductivity.

If energy is expended, and lattice collisions occur, the superconductor will return to its previous state, and lose its superconducting properties.

I think this is how it works.

 

[jules.09]

the BCS theory is soo easy, how can you not get it, the whole ideas module is the easiest section of the course, its just like yr11 chemistry and a light revision of motors and generators with like a few extra concepts, nothing hard

Really? Depends what you mean by getting it. I don't want generic rote learning, I want to actually understand it for what it is. The school version appears flawed, the whole slipstream thing, and diagrams showing cooper pair electrons travelling in the same direction etc.

Do YOU get it?

 

[random-1005]

Really? Depends what you mean by getting it. I don't want generic rote learning, I want to actually understand it for what it is. The school version appears flawed, the whole slipstream thing, and diagrams showing cooper pair electrons travelling in the same direction etc.

Do YOU get it?

an electron moves through the lattice, as the electrons are negative and the ions in the lattice are postive they attract each other (and distort the lattice), creating a region of excess positive charge (hence attracting another electron) which travels closely behind the first one. These form the so called "cooper pairs" and travel through the lattice without collision (hence prefect conductivity).


That is all they would expect in a question. Everything is simplified in high school, the actual mechanics of this is much more complicated (which is the same for all the concepts in physics), but at hsc level this is all they would be looking for.

 

[untouchablecuz]

Discuss the BCS theory.

Þ[FONT=&quot] [/FONT]The BSC theory is a quantum mechanical explanation of superconductivity.
Þ[FONT=&quot] [/FONT]At sufficiently low temperatures, electrons moving through superconducting materials induce vibrations, phonons, in the lattice of positive ions.
Þ[FONT=&quot] [/FONT]These phonons distort the lattice, moving the positive ions towards the electrons as they pass.
Þ[FONT=&quot] [/FONT]This distortion results in a momentary concentration of positive charge behind the electrons.
Þ[FONT=&quot] [/FONT]This positive region attracts a second electron, accelerating it towards the electron in front.
Þ[FONT=&quot] [/FONT]Whilst both the electrons are negatively charged, they attract with phonon-mediated attraction, travelling through the lattice as a Cooper pair.
Þ[FONT=&quot] [/FONT]As these pairs move through the lattice, phonons that are constantly emitted by the electron in front are absorbed by the second electron. This exchange continually distorts the lattice, maintaining electron attraction.
Þ[FONT=&quot] [/FONT]These Cooper pairs move unimpeded by the lattice, causing superconductivity.
Þ[FONT=&quot] [/FONT]As the temperature of the conducting material increases above its critical temperature, the lattice vibrations increase and diminish these Cooper pairs, causing a loss of superconductivity.


thats what i have in my notes, am i correct?

 

[random-1005]

Discuss the BCS theory.

ÞThe BSC theory is a quantum mechanical explanation of superconductivity.
ÞAt sufficiently low temperatures, electrons moving through superconducting materials induce vibrations, phonons, in the lattice of positive ions.
ÞThese phonons distort the lattice, moving the positive ions towards the electrons as they pass.
ÞThis distortion results in a momentary concentration of positive charge behind the electrons.
ÞThis positive region attracts a second electron, accelerating it towards the electron in front.
ÞWhilst both the electrons are negatively charged, they attract with phonon-mediated attraction, travelling through the lattice as a Cooper pair.
ÞAs these pairs move through the lattice, phonons that are constantly emitted by the electron in front are absorbed by the second electron. This exchange continually distorts the lattice, maintaining electron attraction.
ÞThese Cooper pairs move unimpeded by the lattice, causing superconductivity.
ÞAs the temperature of the conducting material increases above its critical temperature, the lattice vibrations increase and diminish these Cooper pairs, causing a loss of superconductivity.


thats what i have in my notes, am i correct?

seems correct

 

[jules.09]

an electron moves through the lattice, as the electrons are negative and the ions in the lattice are postive they attract each other (and distort the lattice), creating a region of excess positive charge (hence attracting another electron) which travels closely behind the first one. These form the so called "cooper pairs" and travel through the lattice without collision (hence prefect conductivity).


That is all they would expect in a question. Everything is simplified in high school, the actual mechanics of this is much more complicated (which is the same for all the concepts in physics), but at hsc level this is all they would be looking for.

It does not travel closely behind, as the textbooks have you believe. The 'coherence length' ranges from hundreds to thousands of ions of electron separation in a Cooper pair.

The reason for this is, if the electrons were too close, their electrostatic repulsion > attractive lattice distortion, causing repulsion, and thus, no superconductivity.

Nor does it travel behind the leading electron. They travel in opposite directions to conserve linear momentum i.e. p = 0.