Talk:Quantum Hall effect

Wiki Education Foundation-supported course assignment - March -> June 2020

This article was the subject of a Wiki Education Foundation-supported course assignment, between 30 March 2020 and 5 June 2020. Further details are available on the course page. Student editor(s): EddySu98.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 07:34, 17 January 2022 (UTC)

Missing Contents

Ther term 'hall conductivity' is never defined. The direction of magnetic field and that of the applied voltage is never mentioned. People use terms like longitutal conductivity and horizontal resistance in QHE studies. None of these terms are defined in this article. —Preceding unsigned comment added by 71.60.19.4 (talk) 02:17, 25 December 2009 (UTC)

Question

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.

Missing science content

Seems very strange to include content on photonic quantum Hall effect (very few experiments exist and it is rather off-topic) but not chern insulators! — Preceding unsigned comment added by 163.1.18.5 (talk) 14:52, 22 September 2023 (UTC)

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)

I added a video that I made. Please let me have feedback. I haven't had a chance to update the text, but I think some updates to the text along the lines of the above warwick uni link would be in order. Perhaps referring to the video where necessary. I was expecting the video to be a bit smaller and on the right. It's a bit vulgar how big it is right now, but maybe someone can change that? Otherwise I'll try to look up how to do it when I get the chance. The "thumb" option was a little extreme, such that you couldn't see anything. Grj23 (talk) 04:41, 4 September 2009 (UTC)

Also, I suppose the same video could be used for the fractional quantum hall effect. It's basically the same thing, except that the lowest landau level splits up because it's composite fermions (electrons bonded to magnetic flux quanta) instead of electrons. —Preceding unsigned comment added by Grj23 (talk • contribs) 04:45, 4 September 2009 (UTC)

Can you modify the video so that the energy of Lowest Landau level also changes with magnetic field ($E_{0}=1/2\hbar \omega$)? In the present form, the Fermi energy can't lie inside the Lowest Landau level states. Prashant

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?

Graphene: QHE at room temp.

The beginning of this article states that QHE is observed in 2d electron systems "subjected to low temperatures and strong magnetic fields". Recent developments (e.g. [[1]]) have shown the QHE in room temperature conditions. Perhaps a good replacement would be the following:

"The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect. It is observed in two-dimensional electron systems usually subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values

   \sigma = \nu \; \frac{e^2}{h}, 

where e is the elementary charge and h is Planck's constant. Recently, the quantum hall effect has also been observed at room temperature in graphene."

Any comments before changing? Or anybody have a better/more apt place to put the graphene developments? -One Son of Ole (talk) 17:56, 26 September 2008 (UTC)

Not simple

The statement that the integer effect can be "simply explained" is false. Simple Landau quantisations would p[roduce precisely quantised plateaus of precisely zero width. The finite width of plateaus requires disorder (and inherently electron scattering, in the face of which precise quantisation is surprising. This article does not explain the origin of this precision nor the not infinitesimal width of plateaus.. —Preceding unsigned comment added by 79.67.70.191 (talk) 20:12, 3 May 2009 (UTC)

Prediction - removed

Quantum Hall effect was not predicted by Ando et al in 1975. I have removed that statement. —Preceding unsigned comment added by 78.86.83.158 (talk) 11:24, 19 July 2009 (UTC)

I remember it differently

It's been a long time, but I remember it differently. I seem to remember, however. When the Nobel Prize was awarded, there was always spoken of resistance, not of the conductivity. Ok, I'll look it up again. --Franz Scheerer (Olbers) (talk) 12:00, 3 November 2013 (UTC)

Sorry, correction

No, the conductance (one divided by the resistance) is 1,2,3, ... times {(1/Rk) = (h/e²)}, according to Nobellecture

"Hall conductivity"?

The so-called "Hall conductivity" in the first sentence should really be "Hall conductance", right? Its units are 1/ohms, not 1/(ohm cm). Or am I misunderstanding? Or is this the usual terminology, even though it's inconsistent with the usual definition of conductance/conductivity? By the way, is it 1/ohms or 1/ohms per square? Thanks! --Steve (talk) 19:32, 13 December 2011 (UTC)

The Hall Voltage is measured orthogonally to the current. I would say, the ratio is neither a resistance nor a conductivity. Yes, certainly not conductivity, but conductance, if at all. --Franz Scheerer (Olbers) (talk) 20:16, 3 November 2013 (UTC)

Actually, because all these systems are 2D, Hall conductivity and conductance have exactly the same units. They are also exactly equal independent of the system size and aspect ratio.

Animation nice but wrong

The animation of the Landau levels as a function of B is nice but wrong. The fermi energy oscillates with them. — Preceding unsigned comment added by 129.27.161.141 (talk) 07:48, 20 January 2012 (UTC)

Several people have pointed out problems with the animation. However, I feel it is still useful despite the issues, and I think we should leave it in place until someone develops a better version. SPat^talk 23:09, 2 August 2014 (UTC)

Bellisard - not the only one

Can I mention once again that, although the noncommutative work by Bellisard is nice, it is not generally considered to be the only explanation of the quantum hall effect. Indeed no one doubted the physics was correct once the original Laughlin gauge argument was in place and Halperin gave a few more details. Few people even know of this work, and to have it feature so prominently in this wikipedia page is just a misrepresentation that keeps re-appearing. — Preceding unsigned comment added by 81.110.91.126 (talk) 20:12, 13 July 2016 (UTC)

Article Organization

At present this article looks highly unorganized. It is unclear exactly what topics this article should cover. For example, the mathematics section looks out of place. The IQHE section doesn't talk about role of disorder at all although the video shows DOS with disorder. There should be separate section for experiments. I propose the following organization.

1. History.

2. Experiments: This section can show the data for IQHE and then say that with purer samples FQHE was also discovered. Further experiments on fractional charges can be mentioned as well.

3. IQHE: This section can talk about Landau levels and how disorder leads to broadening of Landau levels with extended states at the center and localized states at the tails of each Landau level. Laughlin's gauge argument can also be alluded to here to explain why this leads to quantization of Hall conductivity.

4. FQHE: A small section with hyperlink to the full FQHE article. Composite Fermion approach can also be mentioned here.

5. Topological order: Some stuff about Chern number in the current Mathematics section can be moved here. Also, this section can say more things about anyons.

6. Standard of resistance: The applications section can be moved here.

7. Relation to other systems: There can potentially be multiple but short subsections about Quantum Anomalous Hall effect, Quantum Spin Hall Effect, Graphene etc.

What do you think? Let's discuss it further.

Really bad article

The introductory paragraphs are really technical and don't explain anything.

What's the experimental setup? Picture? Geometry? Particles? Participants? Definitions?

Incoherent.

2001:67C:10EC:5787:8000:0:0:8A7 (talk) 10:05, 19 February 2019 (UTC)

Modification of the section Integer Quantum Hall Effect

I am part of a group of Physics students who are finishing the degree this year. We have been asked to modify a Wikipedia article and we have chosen quantum hall effect topic. We have made some brief notes related to the integer quantum hall effect and we would like to add them to the article. In this notes it is explained the explicit derivation of the landau energy expression from Schrödinger’s equation and it is derived explicitly the formula for the conductance that appears at the beginning of the article. Moreover, it is explained how the density of states is related to the number of Landau occupied levels (which may help to understand the video in the article) and it also contains an explanation, not only on the transverse resistivity but also on the longitudinal one. The notes are based on the book: The physics of low-dimensional semiconductors. J. H. Davies. Cambridge University Press. 1998. It would be a pleasure to contribute to this article and I think the modification will make the article more complete in the sense that it lacks mathematical derivations. — Preceding unsigned comment added by Anappzz (talk • contribs) 14:16, 18 May 2020 (UTC)

• What happened ? Were the notes added ? Where can they be seen ? Was the article modified ? - Rod57 (talk) 19:26, 2 July 2024 (UTC)

Error in figure

The figure https://en.wikipedia.org/wiki/File:Rhoxy.jpg is a problem:

• wrong caption: there are no inset
• wrong \rho_xy axis: these are normalized values not kOhms
• the \rho_xx axis should just be considered "arbitrary units" for simplicity — Preceding unsigned comment added by Scharleb (talk • contribs) 01:07, 20 October 2021 (UTC)