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The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures.
Tsui and Störmer made the groundbreaking discovery of the fractional quantum Hall effect in 1982, while Laughlin provided a theoretical interpretation for the discovery the following year. This discovery will eventually be the reason of their winning of the 1998 Nobel Prize in Physics.
In quantum mechanics, fractionalization is the phenomenon whereby the quasiparticles of a system cannot be constructed as combinations of its elementary constituents. One of the earliest and most prominent examples is the fractional quantum Hall effect, where the constituent particles are electrons but the quasiparticles carry fractions of the electron charge.
In 1982, Frank Wilczek published two papers exploring the fractional statistics of quasiparticles in two dimensions, giving them the name "anyons" to indicate that the phase shift upon permutation can take any value. [10] Daniel Tsui and Horst Störmer discovered the fractional quantum Hall effect in
1982 – The fractional quantum Hall effect is discovered by Robert Laughlin, Horst Störmer, and Daniel Tsui. 1982 – First observation of a quasicrystal by Dan Shechtman. [90] 1982 – Frank Wilczek explores the fractional statistics of quasiparticles in two dimensions and coins the term "anyon".
The fractional quantum Hall effect is more complicated and still considered an open research problem. [2] Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect.
1980 – Klaus von Klitzing discovers the quantum Hall effect [24] 1982 – Horst L. Störmer and Daniel C. Tsui discover the fractional quantum Hall effect [25] 1983 – Robert B. Laughlin explains the fractional quantum Hall effect [25] 1986 – Karl Alexander Müller and Georg Bednorz discover high critical temperature ceramic ...
One finds that the different orders in different quantum Hall states can indeed be described by topological orders, so the topological order does have experimental realizations. The fractional quantum Hall (FQH) state was discovered in 1982 [9] [10] before the introduction of the concept of topological order in 1989. But the FQH state is not ...