Re: How can electrons in a superconductive material bind themselves together...

Well Luc, yours is an interesting and rather difficult question. 
Anyway, I'll try to do my best.

The theoretical understanding of superconductivity was advanced in 
1957 by three American physicists -John Bardeen (who also worked on 
developing the first Solid State transistor), Leon Cooper, and John 
Schrieffer-, through their Theory of Superconductivity, known as the 
BCS Theory. BCS Theory is extremely complicated and involves many 
advanced Solid State and Quantum Mechanics topics (Statistical 
Quantum Mechanics, Quantum Lattice Vibrations, Fermion and Boson 
Dynamics, Second Quantization ...).

Nonetheless, a naive picture of Superconductivity can be given by 
using just
Electrostatics.

According to BCS Theory in a superconducting metal electrons seem to 
be in bonded pairs, linked by some attractive force between them. 
These pairs of electrons are known as ''Cooper pairs'', and are 
formed by a couple of electrons with opposite velocities and spin. 

The way electrons are kept together can be thought as follows. As one 
negatively charged electron passes by a positively charged ion in the 
lattice of the superconductor, it attracts the ion, moving it a 
little away from its equlibrium position. Before the electron passes 
by and before the lattice springs get back the ion to its normal 
position, a second electron is attracted by the ion from its new 
position. As a result, an effective force seems to appear between 
electrons that tends to put them both closer (i.e. attractive force).

Maybe the following pictures could help to understand this.

 
      |            |
------o------------o------         o : Metal ions.
      |            |               - : Bondings between ions.
      |            |               e : Electrons in metal.
      |    e       |
      |            |
      |            |
      |            |
------o------------o------
      |            |
      |            |
 e    |            |

-> Step 1: Two electrons with opposite spin and momentum pass by an
           ion in the lattice.


      |            |
------o------------o------
      |            |
      |            |
      |    :       |
      |   :        |
      \  e         |
      .o           |
------/.\----------o------
      |            |
      |            |
 e    |            |

-> Step 2: One of them attracts (and is attracted by) an ion, 
           distorting lattice order.


  
      |            |
------o------------o------
      |            |
      |            |
      |            |
      |            |
      \  e         |
       o           |
------/ \----------o------
   e  |            |
  :   |            |
 :    |            |

-> Step 3: The other electron is attracted towards the moved ion, 
           resulting in an effective attraction between electrons.


 It is through this process that two electrons, which should repel 
one another, link up. It is important to understand, however, that 
the pairs are constantly breaking and reforming. Because electrons 
are indistinguishable particles, it is easier to think of them as 
permanently paired.

The electron pairing is favorable because it has the effect of 
putting the material into a lower energy state and, by pairing off 
two by two, the electrons pass through the superconductor more 
smoothly, avoiding electrons' energy to be lost due to collisions 
with lattice impurities and deffects (that energy lost is what makes 
a metal to be resistive).

As long as the superconductor is cooled to very low temperatures, the 
Cooper pairs stay intact, due to the reduced molecular motion. As the 
superconductor gains heat energy the vibrations in the lattice become 
more violent and break the pairs, so it becomes resistive again. 

I hope this answer has been clear enough, althought it is just an 
oversimplified view of Superconductivity. 

You can find much more details about Superconductivity, as well as 
actual BCS Theory, in many graduate and under-graduate level Solid 
State books (I strongly recommend you C.Kittel's textbook on Solid 
State, as well as N.Ashcroft-D.Mermin's one, which is much more 
mathematical but still good).

Here you have also some links to learn more about Superconductivity:

* http://www.ornl.gov/reports/m/ornlm3063r1/contents.html 
(Oak Ridge National Laboratory - Tennessee, USA.
Complete and quite good teacher's guide to Superconductivity for High
School students, containing theory, applications and developed 
experiments.This has been the main source to my answer, as you can 
see.)

* http://superconductors.org
(Website entirely devoted to Superconductors. Theory, products, links 
...)

Enjoy, ... and keep on thinking.