BCS theory- superconductivity (1 Viewer)

[Akira_Tikira]

I need some help here.

I understand the BCS, and I understand it is a highly quantum mechanic concept. But what I have trouble comprehending because I am thinking Newtonian Physics is that if the lattice is being distorted then isn't the electron doing work on the lattice. This means energy should be lost to the lattice and the electrons should slow down, until it stops.

Obviously this doesn't happen, now there must be some mechanism at which the energy must be returned to the lattice. Jacaranda speaks of soemthing called a phonon.....I don't think I understand it....maybe someone can tell me why...

The syllabuse ask us to discuss the BCS theory, which implies we have to mention advantages and disadvantages....

What are some disadvantages

 

[Giant Lobster]

Yes the lattice is being distorted by the mutual electrostatic attraction between lattice nuclei and a passing electron pair (cooper pair bounded by a phonon) but its obvious if you look at a diagram that the force vectors are all in opposing directions and thus have no net force acting on the electron pair. So no work is being done as the electron moves through a lattice 'tunnel' because the forward and backward electrostatic pulls are the same and cancel out.

 

[Constip8edSkunk]

the proper explaination of the BCS theory goes way beyond the syllabus requirement i think

the feeling i get is that classical phys wont explain this properly (just my feeling, not validated or nething) cuz i remembered i read sumwhere that the cooper pairs are not fermions so paulis exclusion principle dun apply and shit like that which rnt explained in classical phys

i dun really get the phonons either. apparently it is a package of acoustic energy inherent superconductor due to lattice vibration. somehow this is emitted when the lattice distorts due 2 the 1st electron and forms a +ively charged 'trough' around the 1st electron (WTF???? this is what i dun get, can sum1 explain this) which will attract the next electrons so it encompasses the 2 and drag em 2gether until 2nd e- absorbs the phonon energy and they get pulled aprt again, rince dry repeat etc through out the conduction

for that pt i wrote about how the BCS theory only explained 4 Type I superconducers and it must b improved/manipulated or a new theory must b devised 2 encompass type II superconductors and HTSs. on this pt, does any one know if there are experimental validations of the BCS theory

 

[Giant Lobster]

Oh I forgot to mention:

A phonon is a packet of sound energy. But don't think of it as a particle, think of it as a mechanical wave that ripples along a lattice as a cooper pair moves by.
The peaks of the wave are between each electron of a pair and electrostatic attraction binds the pair, and this is a cooper pair.
Its hard to describe in words but I have jacaranda too, and theres diagrams that depict what I have said... hope it helps.

 

[Constip8edSkunk]

yes i hav jacaranda and saw the picture, but how does it form the positive "trough"? and why does it bind around the 1st electron, not the area where the 1st electron passes?

if it is a mechanical wave does taht mean that if u place the superconductor in a vacuum, it would lose its superconductivity?

[EDIT]: i would understand if it is the lattice distorting inwards which all the diagram shows, but how does the phonon comes in? is the charge attracting transmitted via the phonon? is the phonon +ive charged??? how can it b charged if it is a wave? so its another representation of duality of particle/wave so nvm bout that.... but the phonon the method of transfering the postive charge of the ions in the lattice 2 the cooper pair.... HOW? thats the question

 

[Giant Lobster]

Im not sure what ur asking but by the look of ur post i think ur thinking wayyy to complex

My understanding is that a phonon is just what they call a 'packet' of vibration through the lattice. Think of lattice rows as tensioned ferromagnetic ropes (using 2 for simplicity) and an electron a magnet. Assuming the magnet wont just stick onto the rope, (I cant explain that but its the same reason why electrons dont fall into the nucleus during 'orbit') as it passes by, it distorts the ropes around it, inwards. Theres a small lag and so the distortion is slightly behind the magnet. Then another magnet follows behind it and is attacted by the relatively closer inward peaks caused by the first. This is what binds them. No work is being done because despite the fact that the lattice is constantly being distorted, think of it as plucking a guitar string in perfect vacuum. Given this, you can just view the two magnets and the distortion ripple as one 'object' and... yeah, thats how I imagine it to be.

The phonon can be thought to possess charge because it is an inward distortion of positive lattice nuclei, and they are surely charged.

 

[pigs_can_fly]

as the first electron passes through the lattice, the positive ions are attracted to it, but because they are much heavier, they lag behind the electron forming a concentration of positive charge behind it. this then accelerates the electron following, and so the two electrons travel as a Cooper pair through the lattice. i think the 'phonon' can be thought of as a sort of sound wave, but obviously inaudible to human ears. i think they either induce or assist the movement of the positive ions, and cooper pairs are created through 'phonon mediated attraction'. apparently exclusion principle isnt broken because the two electrons in a cooper pair are of opposite spin and momentum, and thus have different quantum numbers. i don't think there has been any empirical evidence, and BCS only applies to low critical temp superconductors, where there is minimal lattice vibration to break up the Cooper pairs. in such superconductors, all the electrons form pairs, but in the more recent high temp superconductors, only some do, and there is yet to be a decent theory to explain superconductivity in those materials.

and constipated skunk, you'd be surprised but macmillan gives a pretty good (albeit very brief) explanation

 

[Constip8edSkunk]

yeah i read that... But how does the phonon transfer the lattice's +ve energy to form a field around the electron.

i mean if they just explain iy without describing phonons i would understand but not when they put the phonon in >_<

but yeah thanx for taking the time 2 answer my posts.

 

[pigs_can_fly]

i think the phonon can be sort of imagined as a disturbance travelling behind the moving electron, bringin the +ve ions slightly behind the electron and thus forming a concentrated =ve region behind it. really, i think its just a term for how the electron attracts the +ve ions but they lag behind. from afar, it looks like a wave forming behind the electron, since the ions obviously return to their rest positions

 

[inasero]

err john ur making things waaaaay too complex as usual...can't u just accept the fact that they are packets of sound energy which bind electrons in a cooper pair together? as far as i know, the syllabus does not require to go into a terrible amount of detail on WHAT phonons since the emphasis is on HOW they interact with the cooper pair, implications for superconductors, etc....

if u tried studying all aspects of the syllabus in detaoil, then obviously you're digging yourself into a hole....

 

[+:: $i[Q]u3 ::+]

i thought it was like... the positive "trough" is formed by the cations in the lattice, which attracts the electrons.
and then the vibration produced as the trough forms releases phonons (sound energy packets) is absorbed by that second electrons, so it follows the first electron along... it's like riding a wave... ???
i could be wrong tho...

 

[Giant Lobster]

yeh its riding a wave basically.

I had a really comprehensive site that explained superconductivity and cooper pairs... cant seem to find it just yet, but i remember it was linked off howstuffworks.com which itself has an adequate explanation.

 

[inasero]

disadvantages are that scientists are still trying to explain how the phonon interactions work~