No Bose-Einstein Condensate in BCS superconductor theory

[Enthalpy]

Hello you all!

 

The Bardeen-Cooper-Schrieffer theory (BCS) makes nice explanations and predictions for the behaviour of traditional superconductors. It relies on electrons making pairs at cold - and pairs of fermions are bosons.

 

Some texts about BCS claim that the electron pairs build a Bose-Einstein Condensate (BEC); other texts don't.

Hyperphysics yes, en.wiki yes, de.wiki yes, es.wiki no, fr.wiki "some analogy", it.wiki no, pt.wiki no - textbooks diverge as well.

 

So I wanted to check whether the original BCS theory did include the BEC of electron pairs. Here are the Nobel lectures by Bardeen, Cooper and Schrieffer:

NobelLecture1972BardeenCooperSchrieffer.zip

which can also be found on the Nobel website:

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-lecture.pdf

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/cooper-lecture.pdf

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/schrieffer-lecture.pdf

 

The clearest part about this point is from Schrieffer on page 105:

The idea that electron pairs were somehow important in superconductivity has been considered for some time (16, 17). Since the superfluidity of liquid He-4 is qualitatively accounted for by Bose condensation, and since pairs of electrons behave in some respects as a boson, the idea is attractive. The essential point is that while a dilute gas of tightly bound pairs of electrons might behave like a Bose gas (18) this is not the case when the mean spacing between pairs is very small compared to the size of a given pair. In this case the inner structure of the pair, i.e., the fact that it is made of fermions, is essential; it is this which distinguishes the pairing condensation, with its energy gap for single pair translation as well as dissociation, from the spectrum of a Bose condensate, in which the low energy excitations are Bose-like rather than Fermi-like as occurs in actual superconductors.

 

So the BEC, which was part of previous superconductor theory, is explicitly excluded by BCS. Because the pairs are big and close to an other, they don't condensate as bosons into a single state. And even: this is necessary to the theory.

[Sensei]

When material has low temperature, its molecules have low velocity.

At 0 K they have velocity close to 0 m/s (which means they have the same speed as Earth at given latitude & height).

 

If we will pass current (electrons) through such material, chance to collide between nucleus and electrons are minimal (as nucleus barely move in crystals).

Which means electrons have little chance to give their kinetic energy to nucleus and being decelerated.

 

It's kinda analogous situation as with transparent materials and light. (theoretically) perfectly transparent material will not absorb energy from incoming photons, and pass they through without any lost of energy.