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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.
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 ...
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.
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 ...
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.
The Chern–Simons term can also be added to models which aren't topological quantum field theories. In 3D, this gives rise to a massive photon if this term is added to the action of Maxwell's theory of electrodynamics. This term can be induced by integrating over a massive charged Dirac field. It also appears for example in the quantum Hall ...