Superconductivity and Fermi levels

[SockCymbal]

So, according to the Fermi function, the higher the temperature of a semiconductor, the higher the likelihood that the electrons can jump to the conduction band. But in superconductors, obviously the temperature is extremely low, so how does the Fermi level, band gap theory, and superconductivity relate?

 

[shawl]

The single electron are located above the energy gap, and the paired electrons (superconducting electrons) are located below the gap.

Under the superconducting transition temperature, the paired electrons will be de-paired with the temperature increasing. That means more superconducting electrons under the gap will be generated into the single electron state which is above the gap.

With the temperature increasing, the single electron distribution is obviously increasing, also.

 

[BANG!]

how does the Fermi level, band gap theory, and superconductivity relate?

Superconductivity is not a bandstructure phenomenon. The principle is entirely different. Namely, a net positive attraction between electrons causes a gapped ground state to form. This has been proven to be generally true, and in the case of conventional superconductors, phonons mediate this attraction. This energy gap results in electrons condensing into pairs. Excitaions within the solid are not sufficient to overcome this gap and so these paired electrons are able to travel through the solid without interacting (scattering) off anything else present in the solid. Technically, it is not so much that this gap is so massive that it dwarfs all the would be excitations. Instead it is the quantum coherence of the superconducting pairs that keeps them from scattering. ie: if you want to scatter one pair then you would have to scatter all of them.

BANG!

 

[DrDu]

Usually, superconductors aren't semi-conductors but metals.