Question

Using the difference between FD statistics for electrons and BE statistics for Cooper pairs, explain superconductivity.

Answer 1

BCS, this is Bardeen, Cooper and Schrieffer. Bardeen, Cooper and Schrieffer, they came up with a theory that help explain a superconductivity still it only explain superconductivity for the original set of materials where you know the temperature the critical temperature was of the order of a few Kelvin. So, this theory for example, is unable to explain how a material at say 90 Kelvin or 100 Kelvin or there about can show you superconductivity. So, therefore, this even at this stage even though this is successfully explain low temperature superconductivity, there is no there is still no accepted theory that explain high temperature superconductivity convincingly. So, that is the that is the state it is in and the way they explained it is that they said in terms of a theory, they theorized that there were pairs of electrons, that sort of operated in a coordinated way and these pairs of electrons were attributes this idea was attributed to Coopers. So, they are called Cooper pairs and it requires the electrons to have opposites spins and opposite k vectors. So, the pairs of electrons would have opposite spins and opposite k vectors and as a result of opposites spins it would as a result of this combination it would appear as though the net k vector was 0 and the net spin was 0. So, suddenly form from electron which is a half spin half integer spin particle, we are having some kind of a composite particle. You can image it in as a some kind of a composite particle which is operating as this pair where the taken together, their net spin is now an integer spin.

So, what was the half integer spin suddenly becomes an integer spin. So, what was half becomes 0, plus or minus half become 0. The important thing about this is that when you go from half to 0 the qualitative difference the specific difference that comes in is that when it is a half spin particle it follows the Fermi Dirac statistics which is what we have discussed in great detail early on. And for a particle to qualify as a Fermion. So, that it follows this Fermi Dirac statistics the requirement is that the the spin should be a half integer spin which is what is true is for an electron, but when you take a pair of electrons especially a pair of this sort where this spins are opposed to each other and the net spin for that then looks like a 0 spin, it was suddenly become an integer spin particle. So, it or it behaves like an integer spin particle, if they are really coordinated, if they really have linked up with each other in some fundamental sense. So, then it behaves like an integer spin particle at which point the statistical behaviour of the set of particles changes.

So, that from being up Fermion, the Cooper pair. So, and is an individual electron is a Fermion and it follows Fermi Dirac statistics, but Cooper pair of electrons which now has an integers spin behaves like set of particles which are called bosons.

The theory says that there are cooper pairs of electrons which have opposite spin, opposite k vectors. So, they behave as though they have no net spins and no net k vector and they are Bosons, they avoid lot of the scattering events in the in the material and they are able to they have certain distance associated with them and so they are able to travel long through the system and as you raise the temperature, if you provide enough energy you break down this pair and that is when the superconducting state suddenly fails, but importantly the all these ideas trace themselves back to the Meissner effect