Editing Quantum Hall effect (section)

== History ==
In 1957, [[Carl Frosch]] and Lincoln Derick were able to manufacture the first [[silicon dioxide]] field effect transistors at [[Bell Labs]], the first transistors in which drain and source were adjacent at the surface.<ref>{{Cite journal |last1=Frosch |first1=C. J. |last2=Derick |first2=L |date=1957 |title=Surface Protection and Selective Masking during Diffusion in Silicon |url=https://iopscience.iop.org/article/10.1149/1.2428650 |journal=Journal of the Electrochemical Society |language=en |volume=104 |issue=9 |pages=547 |doi=10.1149/1.2428650|url-access=subscription }}</ref> Subsequently, a team demonstrated a working [[MOSFET]] at Bell Labs 1960.<ref>{{Cite journal |last=KAHNG |first=D. |date=1961 |title=Silicon-Silicon Dioxide Surface Device |url=https://doi.org/10.1142/9789814503464_0076 |journal=Technical Memorandum of Bell Laboratories |pages=583–596 |doi=10.1142/9789814503464_0076 |isbn=978-981-02-0209-5|url-access=subscription }}</ref><ref>{{Cite book |last=Lojek |first=Bo |title=History of Semiconductor Engineering |date=2007 |publisher=Springer-Verlag Berlin Heidelberg |isbn=978-3-540-34258-8 |location=Berlin, Heidelberg |page=321}}</ref> This enabled physicists to study [[Two-dimensional electron gas|electron behavior in a nearly ideal two-dimensional gas]].<ref name="Lindley">{{cite journal |last1=Lindley |first1=David |title=Focus: Landmarks—Accidental Discovery Leads to Calibration Standard |journal=[[Physics (magazine)|Physics]] |date=15 May 2015 |volume=8 |page=46 |url=https://physics.aps.org/articles/v8/46 |doi=10.1103/physics.8.46|url-access=subscription }}</ref> 

In a MOSFET, conduction electrons travel in a thin surface layer, and a "[[Metal gate|gate]]" voltage controls the number of charge carriers in this layer. This allows researchers to explore [[quantum effects]] by operating high-purity MOSFETs at [[liquid helium]] temperatures.<ref name="Lindley" />

The integer [[Quantization (physics)|quantization]] of the Hall conductance was originally predicted by [[University of Tokyo]] researchers Tsuneya Ando, Yukio Matsumoto and Yasutada Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true.<ref name=Ando:1975 /> In 1978, the [[Gakushuin University]] researchers Jun-ichi Wakabayashi and Shinji Kawaji subsequently observed the effect in experiments carried out on the inversion layer of MOSFETs.<ref name=Wakabayashi:1978 />

In 1980, [[Klaus von Klitzing]], working at the high magnetic field laboratory in Grenoble with [[silicon]]-based MOSFET samples developed by [[Michael Pepper]] and Gerhard Dorda, made the unexpected discovery that the Hall resistance was ''exactly'' quantized.<ref name=vonKlitzing:1980 /><ref name="Lindley"/> For this finding, von Klitzing was awarded the 1985 [[Nobel Prize in Physics]]. A link between exact quantization and gauge invariance was subsequently proposed by [[Robert B. Laughlin|Robert Laughlin]], who connected the quantized conductivity to the quantized charge transport in a Thouless charge pump.<ref name=Laughlin:1981 /><ref name=Thouless:1983 /> Most integer quantum Hall experiments are now performed on [[gallium arsenide]] [[heterostructure]]s, although many other semiconductor materials can be used. In 2007, the integer quantum Hall effect was reported in [[graphene]] at temperatures as high as room temperature,<ref name=Novoselov:2007 /> and in the [[magnesium]] [[zinc]] [[oxide]] ZnO–Mg<sub>''x''</sub>Zn<sub>1−''x''</sub>O.<ref name=Tsukazaki:2007 />