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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.
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
Quantum anomalous Hall state: A state which has a quantized Hall resistance even in the absence of external magnetic field. Topological insulator: a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor. Fractional Chern insulator: A generalization of fractional quantum Hall state to ...
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 ...
In ferromagnetic materials (and paramagnetic materials in a magnetic field), the Hall resistivity includes an additional contribution, known as the anomalous Hall effect (or the extraordinary Hall effect), which depends directly on the magnetization of the material, and is often much larger than the ordinary Hall effect.