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What (who) is quantum constant - definition
![Occupation of Landau levels in a magnetic field neglecting the spin splitting, showing how the [[Fermi level]] moves to maintain a constant density of electrons. The fields are in the ratio <math>2:3:4</math> and give <math>\nu=4,\frac{8}{3}</math> and <math>2</math>.](https://commons.wikimedia.org/wiki/Special:FilePath/NivelesLandausinspin.jpg?width=200 "Occupation of Landau levels in a magnetic field neglecting the spin splitting, showing how the [[Fermi level]] moves to maintain a constant density of electrons. The fields are in the ratio <math>2:3:4</math> and give <math>\nu=4,\frac{8}{3}</math> and <math>2</math>.")
![Plaque at the [[Humboldt University of Berlin]]: "Max Planck, who discovered the elementary quantum of action ''h'', taught here from 1889 to 1928."](https://commons.wikimedia.org/wiki/Special:FilePath/Max Planck Wirkungsquantums 20050815.jpg?width=200 "Plaque at the [[Humboldt University of Berlin]]: \"Max Planck, who discovered the elementary quantum of action ''h'', taught here from 1889 to 1928.\"")
![Intensity of light emitted from a [[black body]]. Each curve represents behavior at different body temperatures. The Planck constant ''h'' is used to explain the shape of these curves.](https://commons.wikimedia.org/wiki/Special:FilePath/Wiens law.svg?width=200 "Intensity of light emitted from a [[black body]]. Each curve represents behavior at different body temperatures. The Planck constant ''h'' is used to explain the shape of these curves.")
Wikipedia
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values
where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,...) values. Here, ν is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively.
The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization).
The fractional quantum Hall effect is more complicated and still considered an open research problem. Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.
