Fermi statistics in experiments

[jostpuur]

In what kind of experiments does the fermi statistics show? What kind of experiments have been carried out to verify that electrons obey fermi statistics? This fermi statistics stuff has been quite theoretical only in texts I have encountered so far.

 

[Gokul43201]

Virtually every single transport measurement (thousands upon thousands of publications each year) out there probes the behavior of electrons living near the Fermi surface.

 

[jostpuur]

Before I had learned about the Maxwell-Bolzmann distribution for the gases, I thought it is a kind of subject where we could have only bad models that somehow predict location of the peak of energy distribution, and comparing the model to the actual measured distributions would be like "bump here and bump there, they about in the same place so it is good model!", but as it turned out it's not like this. The measured distribution has precisly the same shape (meaning that the difference doesn't show in a figures of reasonable accury), which is very impressing.

I don't have the Kittel's book right here, but I remeber reading it, and it explained how the Pauli principle was used to explain behaviour of the electrons in solid, and how most of the electrons cannot get onto higher energy levels because only those near the fermi surface are mobile. However, the electron gas assumption, where we assume that the electrons are not interacting, sounds very strange because aren't the interacting quite strongly in reality? To me, this model of electrons in solid sounds very qualitative. I'm now interested to know, if the Fermi statistics has been verified by experiment equally convincingly as the Boltzmann statistic has been. Or is it giving merely qualitative explanations?

 

[olgranpappy]

However, the electron gas assumption, where we assume that the electrons are not interacting, sounds very strange because aren't the interacting quite strongly in reality?

Yes, it is very strange that the model works at all. To understand why this could ever be possible one should learn about (Landau's) Fermi-Liquid Theory.

 

[Cthugha]

In what kind of experiments does the fermi statistics show? What kind of experiments have been carried out to verify that electrons obey fermi statistics?

For example a strong difference between fermi-dirac statistics and bose-einstein-statistics shows in antibunching/bunching behaviour.

Although it is not about electrons, but helium 3 (fermionic) and helium 4 (bosonic), this paper might be very interesting for you:

Comparison of the Hanbury Brown–Twiss effect for bosons and fermions
T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect and C. I. Westbrook
Nature 445, 402-405 (25 January 2007)

also available at arxiv.org:
http://arxiv.org/abs/cond-mat/0612278

 

[Gokul43201]

However, the electron gas assumption, where we assume that the electrons are not interacting, sounds very strange because aren't the interacting quite strongly in reality?

It turns out that the interactions are not very strong in most typical cases (eg: in an alkali metal), but are not terrible weak either. As granpappy points out, why the free electron approximation works is explained by Landau - the interactions between single particles can be cleverly accounted for by replacing each single particle with a "quasiparticle" whose properties incoporate the particle-particle interactions. In a metal, the quasielectrons then turn out to behave very much like the non-interacting electrons of a Fermi gas, which is why a naive Drude calculation often gives a surprisingly good result for electrical properties.