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Encyclopedia > Quantum Hall effect

The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance $,sigma$ takes on the quantized values Fig. ... Hall effect diagram, showing electron flow (rather than conventional current). ... A two dimensional electron gas (2DEG) is a gas of electrons free to move in two dimensions, but tightly confined in the third. ... Fig. ... In physics, a magnetic field is an pseudovector field that traces out solenoidal lines of force in and around closed electric circuits and bar magnets. ... Electrical conductance is the reciprocal of electrical resistance. ...

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

where $,e$ is the elementary charge and $,h$ is Planck's constant. In the "ordinary" quantum Hall effect, known as the integer quantum Hall effect, $,nu$ takes on integer values ( $,nu$ = 1, 2, 3, etc.). There is another type of quantum Hall effect, known as the fractional quantum Hall effect, in which $,nu$ can occur as a fraction ( $,nu$ = 2/7, 1/3, 2/5, 3/5, 5/2 etc.) The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... The integers are commonly denoted by the above symbol. ... The quantum Hall effect is a quantum mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance &#963; takes on the quantized values where e is the elementary charge and h is Plancks... In common usage a fraction is any part of a unit. ...

The 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 $,{e^2}/{h}$ 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 standard for electrical resistance: the resistance unit $,h/{e^2}$, roughly equal to 25812.8 ohms, is referred to as the von Klitzing constant RK (after Klaus von Klitzing, the discoverer of exact quantization) and since 1990, a fixed conventional value RK-90 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. In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... The ohm (symbol: Î©) is the SI unit of electric resistance. ... Klaus von Klitzing, (born June 28, 1943 in German occupied Åšroda Wielkopolska) is a German physicist. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ...

The integers that appear in the Hall effect are examples of topological quantum numbers. They are known in mathematics as the first Chern numbers and are closely related to 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 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.

The fractional effect is due to somewhat different physics, and was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard. The effect was explained by Robert B. Laughlin in 1983, using a novel quantum liquid phase that accounts for the effects of interactions between electrons. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work. Although it was generally assumed that the discrete resistivity jumps found in the Tsui experiment were due to the presence of fractional charges (i.e., due to the emergence of quasiparticles with charges smaller than an electron charge), it was not until 1997 that R. de-Picciotto, et al., indirectly observed fractional charges through measurements of quantum shot noise. Fractionally charged quasiparticles are neither Bosons nor Fermions and exhibit anyonic statistics. The fractional quantum Hall effect continues to be influential in theories about topological order. Certain fractional quantum Hall phases appear to have the right properties for building a topological quantum computer Daniel Chee Tsui &#23828;&#29734; (pinyin: Cu&#299; Qí)(born February 28, 1939, Henan Province, China) is a Chinese American physicist whose areas of research included electrical properties of thin films and microstructures of semiconductors and solid-state physics. ... Horst Ludwig StÃ¶rmer (born April 6, 1949 in Frankfurt, Germany) is a German physicist who shared the 1998 Nobel Prize in Physics with Daniel Tsui and Robert Laughlin. ... This article is about the chemical compound. ... An area location represented by a point, or a line segment that is bound or unbound, or a plane surface bound or unbound, or a structure that can be represented by multi-plane surfaces that bounds the contained area. ... Arthur Gossard is a professor of Materials at the University of California, Santa Barbara. ... Robert Betts Laughlin (born November 1, 1950) is an American theoretical physicist who, with Horst L. StÃ¶rmer and Daniel C. Tsui, was awarded the 1998 Nobel Prize in physics for his explanation of the fractional quantum Hall effect. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... Photon noise simulation. ... In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... In mathematics and physics, an anyon is a type of projective representation of a Lie group. ... In physics, topological order is a new kind of order (a new kind of organization of particles) in a quantum state that is beyond the Landau symmetry-breaking description. ... A topological quantum computer is a theoretical quantum computer that uses quasiparticles called anyons where their world lines form threads that cross over one another to form braids in a two-dimensional world. ...

• T. Ando, Y. Matsumoto, and Y. Uemura, J. Phys. Soc. Jpn. 39, 279 (1975) DOI:10.1143/JPSJ.39.279
• K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980) DOI:10.1103/PhysRevLett.45.494
• R.B. Laughlin, Phys. Rev. B. 23, 5632 (1981) DOI:10.1103/PhysRevB.23.5632
• D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982) DOI:10.1103/PhysRevLett.48.1559
• R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983) DOI:10.1103/PhysRevLett.50.1395
• R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Nature 389, 162-164 (1997)
• K. von Klitzing, 25 years of Quantum Hall Effect, Poincaré Seminar (Paris-2004). Postscript.
• Magnet Lab - Quantum Hall Effect Observed at Room Temperature
• K. S. Novoselov et al, Science 315 1379 (9 Mar 2007)
• J. E. Avron, D. Osacdhy and R. Seiler, Physics Today, August (2003)

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