Physics:Quantum Hall effect - Revision history

WikiHarold: Remove imported red links from Quantum page

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	The quantization of the Hall conductance (<math> G_{xy}= 1/R_{xy} </math>) has the important property of being exceedingly precise.<ref>{{Cite journal \|last=von Klitzing \|first=Klaus \|date=2005-09-15 \|title=Developments in the quantum Hall effect \|url=https://royalsocietypublishing.org/doi/10.1098/rsta.2005.1640 \|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences \|language=en \|volume=363 \|issue=1834 \|pages=2203–2219 \|doi=10.1098/rsta.2005.1640 \|pmid=16147506 \|bibcode=2005RSPTA.363.2203V \|issn=1364-503X\|url-access=subscription }}</ref> Actual measurements of the Hall conductance have been found to be integer or fractional multiples of {{math\|{{sfrac\|''e''<sup>2</sup>\|''h''}}}} to better than one part in a billion.<ref>{{Cite journal \|last1=Janssen \|first1=T J B M \|last2=Williams \|first2=J M \|last3=Fletcher \|first3=N E \|last4=Goebel \|first4=R \|last5=Tzalenchuk \|first5=A \|last6=Yakimova \|first6=R \|last7=Lara-Avila \|first7=S \|last8=Kubatkin \|first8=S \|last9=Fal'ko \|first9=V I \|date=2012-06-01 \|title=Precision comparison of the quantum Hall effect in graphene and gallium arsenide \|url=https://iopscience.iop.org/article/10.1088/0026-1394/49/3/294 \|journal=Metrologia \|volume=49 \|issue=3 \|pages=294–306 \|doi=10.1088/0026-1394/49/3/294 \|issn=0026-1394\|arxiv=1202.2985 \|bibcode=2012Metro..49..294J }}</ref> It has allowed for the definition of a new practical standard for electrical resistance, based on the resistance quantum given by the '''von Klitzing constant''' {{math\|''R''<sub>K</sub>}}. This is named after [[Biography:Klaus von Klitzing\|Klaus von Klitzing]], the discoverer of exact quantization. The quantum Hall effect also provides an extremely precise independent determination of the fine-structure constant, a quantity of fundamental importance in [[Physics:Quantum electrodynamics\|quantum electrodynamics]].		The quantization of the Hall conductance (<math> G_{xy}= 1/R_{xy} </math>) has the important property of being exceedingly precise.<ref>{{Cite journal \|last=von Klitzing \|first=Klaus \|date=2005-09-15 \|title=Developments in the quantum Hall effect \|url=https://royalsocietypublishing.org/doi/10.1098/rsta.2005.1640 \|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences \|language=en \|volume=363 \|issue=1834 \|pages=2203–2219 \|doi=10.1098/rsta.2005.1640 \|pmid=16147506 \|bibcode=2005RSPTA.363.2203V \|issn=1364-503X\|url-access=subscription }}</ref> Actual measurements of the Hall conductance have been found to be integer or fractional multiples of {{math\|{{sfrac\|''e''<sup>2</sup>\|''h''}}}} to better than one part in a billion.<ref>{{Cite journal \|last1=Janssen \|first1=T J B M \|last2=Williams \|first2=J M \|last3=Fletcher \|first3=N E \|last4=Goebel \|first4=R \|last5=Tzalenchuk \|first5=A \|last6=Yakimova \|first6=R \|last7=Lara-Avila \|first7=S \|last8=Kubatkin \|first8=S \|last9=Fal'ko \|first9=V I \|date=2012-06-01 \|title=Precision comparison of the quantum Hall effect in graphene and gallium arsenide \|url=https://iopscience.iop.org/article/10.1088/0026-1394/49/3/294 \|journal=Metrologia \|volume=49 \|issue=3 \|pages=294–306 \|doi=10.1088/0026-1394/49/3/294 \|issn=0026-1394\|arxiv=1202.2985 \|bibcode=2012Metro..49..294J }}</ref> It has allowed for the definition of a new practical standard for electrical resistance, based on the resistance quantum given by the '''von Klitzing constant''' {{math\|''R''<sub>K</sub>}}. This is named after [[Biography:Klaus von Klitzing\|Klaus von Klitzing]], the discoverer of exact quantization. The quantum Hall effect also provides an extremely precise independent determination of the fine-structure constant, a quantity of fundamental importance in [[Physics:Quantum electrodynamics\|quantum electrodynamics]].

	{{anchor\|RK-1990}}In 1990, a fixed conventional value {{math\|''R''<sub>K-90</sub> {{=~~}} {{physconst\|RK90\|ref=no~~}}}} was defined for use in resistance calibrations worldwide.~~{{physconst\|RK90\|ref=only}}~~ Later, the 2019 revision of the SI fixed exact values of {{math\|''h''}} and {{math\|''e''}}, resulting in an exact {{math\|''R''<sub>K</sub> {{=}} {{sfrac\|''h''\|''e''<sup>2</sup>}} {{=~~}} {{physconst\|RK\|after=.~~}}}}		{{anchor\|RK-1990}}In 1990, a fixed conventional value {{math\|''R''<sub>K-90</sub> {{=}} }} was defined for use in resistance calibrations worldwide. Later, the 2019 revision of the SI fixed exact values of {{math\|''h''}} and {{math\|''e''}}, resulting in an exact {{math\|''R''<sub>K</sub> {{=}} {{sfrac\|''h''\|''e''<sup>2</sup>}} {{=}} }}

	== Research status ==		== Research status ==
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	== Integer quantum Hall effect ==		== Integer quantum Hall effect ==
	[[File:QuantumHallEffectExplanationWithLandauLevels.ogv\|thumb\|360x360px\|Animated graph showing filling of Landau levels as ''B''<nowiki> changes and the corresponding position on a graph of hall coefficient and magnetic field\|Illustrative only. The levels spread out with increasing field. Between the levels the quantum hall effect is seen. DOS is the density of states. Note however that if the electron density rather than the Fermi energy is hold constant, as in the actual experiments, this graph becomes a straight line. Existence of plateaus cannot be explained by this trivial model.</nowiki>]]

	=== Landau levels ===		=== Landau levels ===
	~~{{Main\|Physics:Landau levels}}~~
	In two dimensions, when classical electrons are subjected to a magnetic field they follow circular cyclotron orbits. When the system is treated quantum mechanically, these orbits are quantized. To determine the values of the energy levels the Schrödinger equation must be solved.		In two dimensions, when classical electrons are subjected to a magnetic field they follow circular cyclotron orbits. When the system is treated quantum mechanically, these orbits are quantized. To determine the values of the energy levels the Schrödinger equation must be solved.

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	\|doi=10.1103/PhysRevB.76.085316}}		\|doi=10.1103/PhysRevB.76.085316}}
	* [[Biography:Emmanuel Rashba\|E. I. Rashba]] and V. B. Timofeev, Quantum Hall Effect, Sov. Phys. – Semiconductors v. 20, pp. 617–647 (1986).		* [[Biography:Emmanuel Rashba\|E. I. Rashba]] and V. B. Timofeev, Quantum Hall Effect, Sov. Phys. – Semiconductors v. 20, pp. 617–647 (1986).

	~~{{Condensed matter physics topics}}~~

	~~[[Category:Hall effect]]~~
	~~[[Category:Condensed matter physics]]~~
	~~[[Category:Quantum electronics]]~~
	~~[[Category:Spintronics]]~~
	~~[[Category:Quantum phases]]~~
	~~[[Category:Mesoscopic physics]]~~
	~~[[Category:Articles containing video clips]]~~

	{{Sourceattribution\|Quantum Hall effect}}		{{Sourceattribution\|Quantum Hall effect}}

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:32:52Z

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WikiHarold: Use Quantum See also index module

2026-05-23T22:20:09Z

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 == See also ==
-{{Div col|colwidth=20em}}
+{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}
 == References ==

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	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
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 {{Short description|Electromagnetic effect in physics}}
 The '''quantum Hall effect''' (or '''integer quantum Hall effect''') is a [[Physics:Quantum mechanics|quantized]] version of the [[Physics:Hall effect|Hall effect]] which is observed in two-dimensional electron systems subjected to low [[Physics:Temperature|temperature]]s and strong [[Magnetic field|magnetic field]]s, in which the Hall [[Physics:Electrical resistance and conductance|resistance]] {{math|''R''<sub>xy</sub>}} exhibits steps that take on the quantized values
 : <math> R_{xy} = \frac{V_\text{Hall}}{I_\text{channel}} = \frac{h}{e^2\nu} , </math>
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 The [[Physics:Fractional quantum Hall effect|fractional quantum Hall effect]] is more complicated and still considered an open research problem.<ref name="Hansson 025005">{{cite journal|first=T.H.| last=Hansson |title=Quantum Hall physics: Hierarchies and conformal field theory techniques|journal=Reviews of Modern Physics|volume=89|issue=25005|date=April 2017| article-number=025005 | doi=10.1103/RevModPhys.89.025005 | arxiv=1601.01697 | bibcode=2017RvMP...89b5005H | s2cid=118614055 }}</ref> Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without [[Physics:Landau quantization|Landau levels]].<ref name=Haldane:1988 /> This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the [[Physics:Quantum spin Hall effect|quantum spin Hall effect]] which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.<ref>{{cite book | first=Zyun F. | last=Ezawa | title=Quantum Hall Effects: Recent Theoretical and Experimental Developments | edition=3rd | publisher=World Scientific | year=2013 | isbn=978-981-4360-75-3}}</ref>
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