Explanation of how superconductivity occurs?

[Tzar]

Would anyone like to suggest an "easy" explanation of how superconductivity occurs? Firstly, how the Cooper pairs form and secondly why that actually results in zero resistance?

This is what I understand: An electron passes through the lattice and destorts it. This creates a region of poisitive charge which accelerates a second electron towards the 1st creating the Cooper pair.

Now, books also go into phonons but I don't understand why they are necessary. Also, why the formation of Cooper pairs actually results in superconductivity I don't understand at all, and few books seem to offer an explanation at all. Please help!

 

[ZapperZ]

Would anyone like to suggest an "easy" explanation of how superconductivity occurs? Firstly, how the Cooper pairs form and secondly why that actually results in zero resistance?

This is what I understand: An electron passes through the lattice and destorts it. This creates a region of poisitive charge which accelerates a second electron towards the 1st creating the Cooper pair.

Now, books also go into phonons but I don't understand why they are necessary.

The destortion or deformation of the lattice ions is a demonstration of the vibrational states that the lattice can support. These vibrational states ARE the phonons. For one electron to pass its effect to another electron, especially when it is zipping by so fast, is via such lattice deformation. Cooper has shown that in an overshielding case, even with the presence of coulombic repulsion between two electrons, there can still be a bound state between these two.

Note that in the original BCS theory, although phonons are the "glue" to the formation of cooper pairs, there really is nothing to prevent something else to come in and act as this glue. Before 1986, we think that only phonons can provide such a thing. It is probably no longer true now since spin-mediated paring is appearing to be the leading candidate in high-Tc superconductors.

Also, why the formation of Cooper pairs actually results in superconductivity I don't understand at all, and few books seem to offer an explanation at all. Please help!

If you look at the BE condensate ground state wavefunction, you will see that it, in the simplest form, is a superposition of plane waves. Now I'm guessing that you have done some QM. If you try to find the average position of a particle described by a plane wave, you'll see that it does NOT have an average position - it's location is undefined and covers the whole region of space. That's the same thing that is going on with a cooper pair. Once it has formed, then it condenses to a BE ground state wherby it is no longer localized, and it has long range coherence. It moves without scattering off the lattice ions anymore. This is the property of a superfluid and a supercurrent.

Zz.

 

[Mozart]

I hope you don't mind if I ask some questions of my own Tzar. I just don't think it would be a good idea for me to start another thread with the same topic.

About 20 minutes ago I started reading about superconductors on the web, and I am left very confused about their fundamental properties.

Do superconductors repel all metals, and magnets? Do they ever attract anything? And how is it that they repel magnets or metals?

When the metals or metaloids are at a very low temperature the atoms arrange in a certain lattice right? Is a lattice just a way of saying the type of shape the atoms make? Now I don't understand why the electrons start moving through the lattice in the first place. What makes the electrons start moving? Is it because electrons in metals are loose, and always move?

Lastly I don't understand why these two sites say the opposite things. http://science.howstuffworks.com/maglev-train.htm Howstuffworks says that maglev trains use electromagnetism to move, and this site http://superconductors.org/Uses.htm says they use superconductors to move, and that electromagnets would waste too much energy as heat or something. What gives?

Thanks.

EDIT: Please continue to answer Tzars questions firstly.

 

[Tzar]

Do superconductors repel all metals, and magnets? Do they ever attract anything? And how is it that they repel magnets or metals?

Superconductors repel magnets. This is simply a consequence of Lenz's Law. When you bring a magnet close to a superconductor it induces a current in it which opposes the motion of the magnet ie repelling it. This occurs even in normal conductors. However, in a superconductor this current will never stop, (since there is no resistance) and thus it will continue repelling the magnet.

 

[ZapperZ]

Superconductors repel magnets. This is simply a consequence of Lenz's Law. When you bring a magnet close to a superconductor it induces a current in it which opposes the motion of the magnet ie repelling it. This occurs even in normal conductors. However, in a superconductor this current will never stop, (since there is no resistance) and thus it will continue repelling the magnet.

Er.. be careful here. Lenz's law only states that there will be an induced field in such a way to prevent a CHANGE in the external field. This means that there will be NO induced field if you just let a magnet sit still in a loop of wire. Only when you move the magnet back and forth (a change in the flux) will you induce a current and consequently a field in that loop of wire.

This is not the case for a superconductor and the Meissner effect. The induced field will still be there even when the external field remains constant. And unlike Lenz's law, when you move the magnet away, the induce current in the superconductor does not try to resist this removal. In fact, it is "happier" that way.

Zz.

 

[Tzar]

Thanks for your reply Zapper, however I'm still confused about a few things:

The destortion or deformation of the lattice ions is a demonstration of the vibrational states that the lattice can support. These vibrational states ARE the phonons.

I don't quite understand this. For some reason I thought phonos were related to sound somehow?? What is a phonon exactly?


For one electron to pass its effect to another electron, especially when it is zipping by so fast, is via such lattice deformation. Cooper has shown that in an overshielding case, even with the presence of coulombic repulsion between two electrons, there can still be a bound state between these two.

Note that in the original BCS theory, although phonons are the "glue" to the formation of cooper pairs, there really is nothing to prevent something else to come in and act as this glue. Before 1986, we think that only phonons can provide such a thing. It is probably no longer true now since spin-mediated paring is appearing to be the leading candidate in high-Tc superconductors.

If you look at the BE condensate ground state wavefunction, you will see that it, in the simplest form, is a superposition of plane waves. Now I'm guessing that you have done some QM. If you try to find the average position of a particle described by a plane wave, you'll see that it does NOT have an average position - it's location is undefined and covers the whole region of space. That's the same thing that is going on with a cooper pair. Once it has formed, then it condenses to a BE ground state wherby it is no longer localized, and it has long range coherence. It moves without scattering off the lattice ions anymore. This is the property of a superfluid and a supercurrent.

Zz.

I have done some QM. (but only a bit) How is the fact that you can't find an everage position related to the fact that the electron passes through without resistance.

Also, is there a non QM explanation?

 

[Tzar]

Er.. be careful here. Lenz's law only states that there will be an induced field in such a way to prevent a CHANGE in the external field. This means that there will be NO induced field if you just let a magnet sit still in a loop of wire. Only when you move the magnet back and forth (a change in the flux) will you induce a current and consequently a field in that loop of wire.

But in order for you to "sit" the magnet on top of the loop, you would have to move it there, thus creating the change of the magnetic field which will induce the current. Isn't that right??

 

[ZapperZ]

I don't quite understand this. For some reason I thought phonos were related to sound somehow?? What is a phonon exactly?

Phonons are, to put it crudely, lattice vibrations. Of COURSE it is related to sound in solids since sound IS lattice vibrations. In fact, a particular phonon mode is sometime called (especially in old solid state texts) as first sound. I recommend you refer to elementary solid state texts such as Kittel.

I have done some QM. (but only a bit) How is the fact that you can't find an everage position related to the fact that the electron passes through without resistance.

When an electron is spread out simultaneously all over the solid, it is not localized. The fact that it remains coherent (i.e. does not lose or slip its phase in the wavefunction) means that it moves without scattering. No scattering means no resistance.

Also, is there a non QM explanation?

According to Carver Mead, superconductivity is the CLEAREST manifestation of quantum phenomenon. It has ZERO classical analogy and classical physics utterly failed, and failed miserably to come close to describing such effects. So no, not only is there no non QM explanation, but there's none even close!

http://www.pnas.org/cgi/content/abstract/94/12/6013?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=carver+mead&searchid=1128387417827_10476&stored_search=&FIRSTINDEX=0&journalcode=pnas

Zz.

 

[ZapperZ]

But in order for you to "sit" the magnet on top of the loop, you would have to move it there, thus creating the change of the magnetic field which will induce the current. Isn't that right??

It doesn't matter. What distinguish this between with Lenz's law is that it doesn't have to CHANGE with time. Lenz's law has a d(flux)/dt requirement. Meissner effect doesn't!

Zz.

 

[Tzar]

It doesn't matter. What distinguish this between with Lenz's law is that it doesn't have to CHANGE with time. Lenz's law has a d(flux)/dt requirement. Meissner effect doesn't!

Zz.

In that case, what does induce the current in the superconductor to produce the Meisnner effect? The enrgy has to come from somwehere...

 

[ZapperZ]

In that case, what does induce the current in the superconductor to produce the Meisnner effect? The enrgy has to come from somwehere...

The external magnetic field!

However, unlike Lenz's law, no energy is needed to SUSTAIN the supercurrent that produces the induced field. So once it is established, it STAYS until something else changes, such as the removal of that external field.

Zz.