Talk:Quantum Hall effect

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The fractional quantum Hall effect says that σ is a multiple of a fraction with an odd denominator of e²/h. Take a large enough denominator and you can make the "quantized" steps as small as you want?!?!

Yep. -- CYD

Then what's the difference to the classical Hall effect? 193.171.121.30 05:12, 14 Dec 2004 (UTC)

Small quantum numbers correspond to low temperatures or high field strengths. As the temperature increases or the field becomes weaker, the quantum Hall effect merges into the classical effect. For example, see here. -- CYD

Yep, but I mean the fractional quantum Hall effect: If ν can take take any values of the form x/(2y+1) then there are no discrete steps which make the quantum Hall effect different from the classical effect. 193.171.121.30 21:55, 15 Dec 2004 (UTC)

Oh, okay. It turns out that "primary" fractions like 1/3 are easy to see, but other fractions like 3/5 and 5/3 are barely distinguishable from the background unless the sample is very pure and the magnetic field is very strong. See here, looking at the roughly 45 degree sloping line, which shows the Hall resistance as a function of the magnetic field. The plateaus are the quantum Hall steps. By "less significant", I'm referring to something called the "hierachy of quantum Hall states" -- excitations like 3/5 are actually built up from the anyon gas of "primary" fractional excitations like 1/3. It's a remarkably beautiful topic. -- CYD

The difference between the fractional and the integer quantum Hall-effect is the difference between integer and fractional numbers. The fractional Hall-effect proves that charges smaller than e kan be found in a 2D electron field (low temperature and a very strong magnetic field), which basically means that this field consists out of quasi-particles, formed by the quantized magnetix flux and the electrons.

[edit] Missing science content

The article appears to be much more about the history of the QHE than about the underlying physics. To me the explanatory science content is a bit skimpy. Nothing about Landau levels, Dingle temperatures, composite fermions, Wigner crystals? The QHE is a pretty deep topic about electrons in solids. This is more helpful to the general physics reader I imagine. Alison Chaiken 21:47, 29 December 2005 (UTC)

[edit] missing image

The article currently mentions "the Azbel-Harper-Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure." However, there are currently no diagrams in the article. Was the diagram accidently deleted?