Fractional quantum Hall effect

A quantum Hall phenomenon in which interacting electrons form collective states whose Hall conductance is quantized to fractional multiples of e²/h. Its excitations can carry fractional charge and obey anyonic exchange statistics.

Landau level: A highly degenerate energy level for charged particles moving in a magnetic field. The fractional states form when electrons partially fill a Landau level.
Filling factor: The ratio of particle density to magnetic flux density, expressed as the number of filled Landau levels. Fractions label how many orbital states are occupied in the partially filled level.
Klaus von Klitzing: German physicist who discovered the integer quantum Hall effect in 1980. His discovery established the quantized Hall setting in which fractional plateaus were later found.
Anyon: A two-dimensional particle whose exchange statistics can take values between those of bosons and fermions. Fractional Hall excitations can acquire fractional statistical phases when exchanged.
Integer quantum Hall effect: A quantum Hall phenomenon in which filled Landau levels produce integer multiples of e²/h in Hall conductance. Its plateaus need no interaction-driven fractionalization of the electron fluid.
Laughlin wavefunction: A many-electron trial state describing incompressible quantum Hall liquids at filling factors 1/(2m+1). It captures the correlations behind the simplest fractional plateaus.
Quantum Hall effect: The quantization of Hall conductance in a two-dimensional electron system under a strong magnetic field. The fractional effect extends this phenomenon beyond integer conductance plateaus.
Daniel Tsui: Chinese-American physicist who co-discovered the fractional quantum Hall effect in 1982. His experiments revealed an unexpected plateau near filling factor 1/3.
Non-Abelian anyon: An anyon whose exchanges act as noncommuting transformations on a degenerate state space. Certain proposed fractional Hall states may host these excitations.
Fractional Chern insulator: An interacting topological phase with fractional Hall-like order in a lattice system without an external magnetic field. It realizes related fractionalized physics without conventional Landau levels.

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