# Cooper Pairing

1. Mar 2, 2004

### Silverious

I'd like to know more about cooper pairing. If anyone has any good resources I'd appreciate it if they shared them. Thanks in advance.

2. Mar 3, 2004

3. Mar 4, 2004

### ZapperZ

Staff Emeritus
I am typically a fan of the Hyperphysics website. It has a wealth of solid info on just about everything and I always recommend people to go there first if they have a question. This, however, is the one exception. The info on Cooper paring is rather vague, and I don't understand this overemphasis on the "band gap"! The existence of the band gap does not automatically imply that these cooper pairs can conduct without resistance. If this were true, than insulators would have the same properties since there's a huge band gap in a typical insulator! In a superconductor, this band gap (more accurately the energy gap in the single-particle band structure) is the energy needed to break apart a cooper pair.

Instead of the hyperphysics site, I would recommend this one. It is low on math (in fact, non-existent), but it has a nice "cartoon" description of one mechanism for the formation of these cooper pairs.

http://www.chemsoc.org/exemplarchem/entries/igrant/bcstheory_noflash.html

Zz.

4. Mar 4, 2004

5. Mar 4, 2004

### ZapperZ

Staff Emeritus
:)

I'm glad you like it. But please make sure you take descriptions like these with a grain of salt. There's nothing in the actual description of this phenomena that says that this is what it exactly looks like.

And the matter is even more complicated for high-Tc superconductors. An example would be that there are strong evidence that the electrons can assembled themselves into "pre-formed" pairs but do not yet form a condensate. This means that you can detect a gap in the energy band, but yet, it is still above the critical temperature for the superconductor. This means that there are "pairs" already, but the material isn't superconducting yet! It needs to go to an even lower temperature before such thing occurs. In conventional superconductor, both pairing and condensing occur at roughly the same temperature, Tc.

It is why this family of material has been keeping condensed matter physicists on their toes ever since they were discovered. The more layers you peel, the more complex and fascinating it becomes!

Zz.

6. Mar 9, 2004

### Silverious

Fascinating indeed. Thank you for the links zapperz and suyver.

7. Apr 14, 2004

### garytse86

what exactly is a band-gap? Is this linked with periodic potential?

8. Apr 14, 2004

### ZapperZ

Staff Emeritus
A band gap is a gap in the material's energy level. In solids, the energy levels are continuous but only over a certain range. In metals, if you estimate the conduction electrons as "free electrons", then you have a dispersion relation looking like

$$E = \hbar^2 k^2/2m$$

This means that E and k are continuous over all range. However, if you turn on the periodic potential, then you no longer have completely free electrons, but rather a "nearly-free" electrons, and your electron wavefunction is now the Bloch wavefunction having the same periodicity. This is where you will start seeing a gap at the zone boundary because only a certain range of k's will be allowed, and that in turn will limit E.

Zz.

Last edited: Apr 14, 2004
9. Apr 15, 2004

### nbo10

In a superconductor the band gap is not caused by a periodic potential but is caused by the electron-phonon interaction.

JMD

10. Apr 15, 2004

### ZapperZ

Staff Emeritus
Er.. not quite. The gap in the energy spectrum of a superconductor is caused by the energy required to break apart a Cooper Pair.

The mechanism for such pairing can be anything. In conventional superconductor, it is the electron-phonon interaction, but in high-Tc superconductors, it can easily be electron-magnon or electron-[insert favorite bosonic excitation here]. Also take note that electron-phonon interaction doesn't always produce a band gap. There are tons of electron-phonon interactions in a normal metal - this is the predominant origin of normal resistivity in metals. Yet, we don't see band gaps arising out of these interactions.

Zz.

11. Apr 24, 2004

### kurious

Is superconductivity associated exclusively with materials which have low entropy.

12. Apr 27, 2004

### clint

entropy

Entropy (or the sum of -p.lnp. over all probabilities p at a given temperature) is determined experimentally by first measuring the specific heat capacity (C), that is, the heat required to raise the temperature of a material a Delta amount (s.i. units of C are of the order 10^-23 joules/kelvin) under given experimental conditions, and then by partially integrating C/T over temperature (starting at near 0K).

As far as the conduction electron contribution to C, as cooper pairs progressively condense below the critical temperature Tc, there is an observed decrease in C/T with decreasing temperature, and thus a drop in the electronic entropy S. These observations are clear in all superconducting materials, conventional or not.

In relation to Zz's statement also, for non conventional high Tc superconductors, there is already an observed loss in entropy in the normal state, ie at temperatures above Tc, due to the "pre-formed" pairs. The onset temperature of this effect is known as the psuedo-gap temperature, T*.

13. Apr 28, 2004

### kurious

If superconductors were made from the heaviest atoms known to science, this would
limit the amplitude of atomic vibration and should increase electronic conductivity at
high temperatures.Is this why most superconductors are heavy materials?

14. Apr 28, 2004

### clint

Not quite.

In conventional superconductors, the electron-electron attraction is a result of the electron-phonon interaction (where a phonon is a quanta of a lattice/atomic vibration), right?

According to conventional superconductor theory then, the onset temperature of superconductivity, Tc, is proportional to the characteristic phonon temperature, so called the Debye temperature Td. Td is in turn proportional to M^-1/2 , where M is the atomic mass of the metal. So in fact, for all other things constant, the lighter the element, or the lower the M, the larger the value of Td and therefore Tc (although Tc has a maximum theoretical value, around 40K or so) for conventional materials.

As for the high temperature normal state, well above Td, the conductivity is dominated by the number of phonons available to limit the mean free path of the conduction electrons, which doesn't depend on the M. Going down the alkali metals column, the conductivity at a fixed temperature, say room temperature, decreases with increasing atomic mass mostly due to the increasing separation between atoms.

The confusion may arise from non-conventional materials, high Tc, where the chemical unit cell is more complicated than in conventional superconductors, and contains heavy elements like Hg, La, etc. amongst the lighter ones like Cu, O. However, the phonon coupling to the conduction electrons is not believed to be the dominant interaction behind superconductivity in this case, and has no theoretical limit to Tc (that we know of).

Last edited: Apr 28, 2004
15. May 5, 2004

### kurious

superconductivity

for all other things constant, the lighter the element, or the lower the M, the larger the value of Td and therefore Tc (although Tc has a maximum theoretical value, around 40K or so) for conventional materials

Would superconductivity be present at higher temperatures than 40K if sound waves were fed into a crystal lattice.Can sound waves increase the phonon quanta by reducing the inertia of atoms?

Last edited: May 5, 2004
16. May 5, 2004

### Silverious

Well, haven't superconductors been made at 150K by adding an Oxygen? Seems like I heard that somewhere.

17. May 5, 2004

### ZapperZ

Staff Emeritus
Most of the high-Tc superconductors (the cuprates) are doped with oxygen to add "holes" to the insulating parent compounds. These are the ones with the highest Tc at optimal doping. There is a sister compound of the cuprates that are electron doped. They tend to not have the same high Tc as the hole doped. There are also indications that their physics may be different than the hole doped.

The 150K superconductor is a Hg-family of hole-doped cuprates, but it gets to 150K Tc only under pressure.

Zz.

18. May 6, 2004

### kurious

Why does high pressure cause superconductivity at higher temperatures?
Does the pressure force electron pairs to stay together?

19. May 20, 2004

### kurious

The copper-oxygen planes that
are believed to be responsible for superconductivity are separated by
many insulating layers layers. So there might not be much overlap between
atomic orbitals between separated Cu-O planes. However, electrons can
still tunnel through the insulating layers. This tunneling is believed
to affect superconductivity, but it is not well understood how.

In type 1 superconductors there are lots of cooper pairs and there is a rapid change in conductivity.Type 2 superconductors show a gradual change from normal to super conductivity .Perhaps type 2 superconductors conduct increasingly better because electron movement through a lattice causes the formation of "groups" of atoms in the lattice which then cause further electron movements in such a way as to increase the formation of yet more groups and so on, as the temperature decreases

20. May 20, 2004

### nbo10

Carefull..... Only a small portion of electrons are invloved in the pairing.

JMD