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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.
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.
The fractional quantum Hall effect of electrons is thus explained as the integer quantum Hall effect of composite fermions. [5] It results in fractionally quantized Hall plateaus at =, with given by above quantized values. These sequences terminate at the composite fermion Fermi sea.
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 ...
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.
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
Fractional excitons are a class of quantum particles discovered in bilayer graphene systems under the fractional quantum Hall effect. These excitons form when electrons and holes bind in a two-dimensional material separated by an insulating layer of hexagonal boron nitride. When exposed to strong magnetic fields, these systems display ...