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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.
Arise in a two-dimensional system subject to a large magnetic field, most famously those systems that exhibit the fractional quantum Hall effect. [4] electron Configuron [5] An elementary configurational excitation in an amorphous material which involves breaking of a chemical bond Cooper pair: A bound pair of two electrons electron Dirac electron
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.
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.
Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 [1] and have been studied more intensely since early 2010. [2] [3] They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial ...
Nobel Lecture: "The fractional quantum Hall effect" by H. L. Stormer "Composite Fermions: New particles in the fractional quantum Hall effect", by H. Störmer and D. Tsui, Physics News in 1994, American Institute of Physics, 1995, p. 33. Composite Fermion at the Pennsylvania State University
In condensed matter physics, the Laughlin wavefunction [1] [2] is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor of the lowest Landau level is = / where is an odd positive integer.
The fractional quantum Hall effect is a topological ordered state which corresponds to patterns of long-range quantum entanglement. [7] States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.