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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 , ν takes on integer values (ν = 1, 2, 3, etc.). There is another type of quantum Hall effect, known as the fractional quantum Hall effect, in which ν can occur as a fraction with an odd denominator (ν = 2/7, 1/3, 2/5, 3/5, etc.)
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˛/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: since 1990, one "klitzing" (after Klaus von KlitzingKlaus von Klitzing (born June 28, 1943 in Schroda, Posen) is a German physicist. For his discovery of the Integer Quantum Hall Effect he was awarded the 1985 Nobel Prize in Physics. After studying physics in Braunschweig, von Klitzing spent 10 research ye, the discoverer of exact quantization) has been defined as the Hall resistance at ν = 4 (i.e., h/4e˛). In addition, the resistance unit h/e˛, roughly equal to 25,812.8 OhmThe ohm is the SI derived unit of electrical resistance (derived from the ampere and the watt). Its symbol is the Greek capital letter omega (Ω). The ohm is named for Georg Ohm, a German physicist who discovered the relation between voltage and currs, is sometimes referred to as the von Klitzing constant. When coupled with measurements of the Josephson constantThe magnetic flux quantum Φ is the quantum of magnetic flux passing through a superconductor. The inverse of the flux quantum, 1/Φ, is called the Josephson constant and is denoted K''. It is a property of a supercurrent (superconducting electrical, it provides an extremely precise independent determination of the fine structure constant, an extremely important quantity in quantum electrodynamicsQuantum electrodynamics QED is a quantum field theory of electromagnetism. QED describes all phenomena involving electrically charged particles interacting by means of the electromagnetic force and has been called "the jewel of physics" for its extremely.
The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975Events January January 1 Watergate scandal: John N. Mitchell, H. Haldeman, John D. Ehrlichman are found guilty of the Watergate cover-up and are sentenced to 30 months to 8 years in jail on February 21 January 5 The Tasman Bridge in Tasmania, Australia, i, on the basis of an approximate calculation. Several workers subsequently observed the effect in experiments carried out on the inversion layer of MOSFETs. It was only in 1980 that von Klitzing, working with samples developed by Michael Pepper and Gerhard Dorda, made the totally 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 Laughlin.
The fractional effect was discovered in 1982 by Daniel Tsui and Horst Störmer , in experiments performed on gallium arsenide heterostructure s developed by Arthur Gossard. The effect was explained by 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.