[theory] formation of cooper pairs

[t_n_p]

Homework Statement

I'm interested to know how cooper pairs are formed in low temperature superconductors.

The Attempt at a Solution

My basic understanding is that electrons will repel other electrons and attract the positive ions which make up the lattice of the metal. The attraction between the +ve ions and the electrons is enough to distort the ions and hence attract other electrons. The attraction due to the displaced ions can then overcome the repulsion between electrons causing them to form cooper pairs. Does this general case apply for low temperature superconductors?

 

[CompuChip]

IIRC that picture, though convenient to make a mental image, is only approximately right. The Cooper pairing between electrons is a purely quantum mechanical effect and one needs the full BCS theory to describe it. The field theoretical description looks quite elegant.

Basically, what happens, is that a small attractive interaction between the electrons takes place (for example in the way you explained in your post, in the case of a crystal lattice). Two electrons can be bound together in a single quantum state (note however, that they can be physically separated by a "large" distance) which has a certain "binding energy". This , as condensed matter people say, opens a gap in the energy spectrum: it takes a certain amount of energy to break this pair. If the temperature is low enough so that thermal fluctuations cannot bridge this gap, the system will form as much of this lower-energy pairs as possible, whence - among other things - the electrical resistance (~ "number of collisions due to thermal fluctuations") drops to zero.

But again, to understand it fully, you should dive into BCS theory (and if you know anything about field theory, I can recommend the field theory approach).