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صفحهٔ جدید: {{جا:ویرایش}} The '''quantum Hall effect''' (or '''integer quantum Hall effect''') is a quantum-mechanical version of the Hall effect, observed...
 
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{{در دست ویرایش ۲|ماه=ژوئن|روز=۱۲|سال=۲۰۰۸|چند = 2}}
'''اثر کوانتمی هال'''{{انگلیسی|quantum Hall effect}} [[مکانیک کوانتم|مکانیک کوانتمی]] از [[اثر هال]] است, که در سیستم‌های دو الکترونی و در [[دما]]ی پایین و [[میدان مغناطیسی]] بالا دیده می شود, به طوری که رسانایی(σ) با مقدارهای زیر برابر می شود
The '''quantum Hall effect''' (or '''integer quantum Hall effect''') is a [[quantum mechanics|quantum-mechanical]] version of the [[Hall effect]], observed in [[2DEG|two-dimensional electron systems]] subjected to low [[temperature]]s and strong [[magnetic field]]s, in which the Hall [[Electrical conductivity|conductivity]] σ takes on the quantized values
 
:<math> \sigma = \nu \; \frac{e^2}{h}, </math>
 
whereکه <math>e</math> is the [[elementaryبار chargeبنیادی]] andو <math>h</math> is [[Planck'sثابت constant]]پلانک. In the "ordinary" quantum Hall effect, known as the integer quantum Hall effect,و ν takesمقادیر onصحیح [[integer]]۱.۲.۳ valuesو ( ν = 1, 2, 3, etc.).. Thereرا isمی anotherتواند typeاختیار ofکند quantum Hall effectو, known as the [[fractionalاثر quantumکسری Hallکوانتمی effectهال]], in which ν canمی occurتواند asمقادیر a [[fraction]]کسری ( νاختیار کندν = 2/7, 1/3, 2/5, 3/5, 5/2 etc...)
 
 
 
==کاربردها==
==Applications==
The [[Quantization (physics)|quantization]] of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of <math>{e^2}/{h}</math> to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of [[gauge invariance]]. It has allowed for the definition of a new practical [[physical unit|standard]] for [[electrical resistance]]: the resistance unit <math>h/{e^2}</math>, roughly equal to 25812.8 [[Ohm (unit)|ohm]]s, is referred to as the von Klitzing constant [http://physics.nist.gov/cgi-bin/cuu/Value?rk|search_for=RK ''R''<sub>K</sub>] (after [[Klaus von Klitzing]], the discoverer of exact quantization) and since 1990, a fixed conventional value [http://physics.nist.gov/cgi-bin/cuu/Value?rk90|search_for=RK ''R''<sub>K-90</sub>] is used in resistance calibrations worldwide. The quantum Hall effect also provides an extremely precise independent determination of the [[fine structure constant]], a quantity of fundamental importance in [[quantum electrodynamics]].
 
==History==
The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation. Several workers subsequently observed the effect in experiments carried out on the inversion layer of [[MOSFET]]s. It was only in 1980 that [[Klaus von Klitzing]], working with samples developed by [[Michael Pepper]] and Gerhard Dorda, made the unexpected discovery that the Hall conductivity was ''exactly'' quantized. For this finding, von Klitzing was awarded the [[1985]] [[Nobel Prize in Physics]]. The link between exact quantization and gauge invariance was subsequently found by [[Robert B. Laughlin|Robert Laughlin]]. Most integer quantum Hall experiments are now performed on [[gallium arsenide]] [[heterostructure]]s, although many other semiconductor materials can be used. Integer quantum Hall effect has also been found in [[graphene]] at temperatures as high as room temperature.
 
==Mathematics==
[[Image:Hofstadter's_butterfly.png|thumb|[[Hofstadter's butterfly]]]]
The integers that appear in the Hall effect are examples of [[topological quantum number]]s. They are known in mathematics as the first [[Chern_class#Chern_numbers|Chern numbers]] and are closely related to [[Geometric phase|Berry's phase]]. A striking model of much interest in this context is the Azbel-Harper-Hofstadter model whose quantum phase diagram is the [[Hofstadter's butterfly]] shown in the figure. The vertical axis is the strength of the [[magnetic field]] and the horizontal axis is the [[chemical potential]], which fixes the electron density. The colors represent the integer Hall conductances. Warm colors represent positive integers and cold colors negative integers. The phase diagram is fractal and has structure on all scales. In the figure there is an obvious [[self-similarity]].
 
==جستارهای وابسته==
Concerning physical mechanisms, impurities and/or particular states (e.g., edge currents) seem to be important for the 'integer' effect, whereas in the [[fractional quantum Hall effect]] the Coulomb interaction is considered as the main reason. Finally, concerning the observed strong similarities between integer and fractional quantum Hall effect, the apparent tendency of electrons, to form bound states of an odd number with a magnetic flux quantum, i.e. ''composite fermions'', is considered.
*[[اثر کسری کوانتمی هال]]
*[[اثر هال]]
 
==See alsoمنابع ==
*[[fractional quantum Hall effect]]
*[[Hall effect]]
 
== References ==
*{{ cite journal | last = Ando | first = Tsuneya | authorlink = | coauthors = Matsumoto, Yukio; Uemura, Yasutada | year = 1975 | month = | title = Theory of Hall Effect in a Two-Dimensional Electron System | journal = [[Journal of the Physical Society of Japan|J. Phys. Soc. Jpn.]] | volume = 39 | issue = | pages = 279&ndash;288 | doi = 10.1143/JPSJ.39.279 | url = | accessdate = | quote = }}
*{{ cite journal | last = Klitzing | first = K. von | authorlink = | coauthors = Dorda, G.; Pepper, M. | year = 1980 | month = | title = New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance | journal = [[Physical Review Letters|Phys. Rev. Lett.]] | volume = 45 | issue = 6 | pages = 494&ndash;497 | doi = 10.1103/PhysRevLett.45.494 | url = | accessdate = | quote = }}
*{{ cite journal | last = Laughlin | first = R. B. | authorlink = | coauthors = | year = 1981 | month = | title = Quantized Hall conductivity in two dimensions | journal = Phys. Rev. B. | volume = 23 | issue = 10 | pages = 5632&ndash;5633 | doi = 10.1103/PhysRevB.23.5632 | url = | accessdate = | quote = }}
*{{ cite journal | last = Yennie | first = D. R. | authorlink = | coauthors = | year = 1987 | month = | title = Integral quantum Hall effect for nonspecialists | journal = Rev. Mod. Phys. | volume = 59 | issue = 3 | pages = 781&ndash;824 | doi = 10.1103/RevModPhys.59.781 | url = | accessdate = | quote = }}
*{{ cite journal | last = Novoselov | first = K. S. | authorlink = | coauthors = ''et al.'' | year = 2007 | month = | title = Room-Temperature Quantum Hall Effect in Graphene | journal = [[Science (journal)|Science]] | volume = 315 | issue = 5817 | pages = 1379 | doi = 10.1126/science.1137201 | url = | accessdate = | quote = }}
*{{ cite journal | last = Hsieh | first = D. | authorlink = | coauthors = ''et al.'' | year = 2008 | month = | title = A topological Dirac insulator in a quantum spin Hall phase | journal = [[Nature (journal)|Nature]] | volume = 452 | issue = 7190 | pages = 970&ndash;974 | doi = 10.1038/nature06843 | url = | accessdate = | quote = }}
* ''25 years of Quantum Hall Effect'', K. von Klitzing, Poincaré Seminar (Paris-2004). [http://parthe.lpthe.jussieu.fr/poincare/textes/novembre2004.html Postscript].
* ''Quantum Hall Effect Observed at Room Temperature'', Magnet Lab Press Release [http://www.magnet.fsu.edu/mediacenter/news/pressreleases/2007february15.html]
* J. E. Avron, D. Osacdhy and R. Seiler, Physics Today, August (2003)
{{یاکرد-ویکی|پیوند=|عنوان=quantum Hall effect |تاریخ بازیابی=۱۲ ژوئن ۲۰۰۸}}
 
[[رده:الکترونیک کوانتمی]]
[[Category:Hall effect]]
[[Category:Condensed matter physics]]
[[Category:Quantum electronics]]
[[Category:Spintronics]]
 
[[da:Kvante Hall-effekten]]
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