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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.
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.
Robert Betts Laughlin (born November 1, 1950) is the Anne T. and Robert M. Bass Professor of Physics and Applied Physics at Stanford University. [1] Along with Horst L. Störmer of Columbia University and Daniel C. Tsui of Princeton University, he was awarded a share of the 1998 Nobel Prize in physics for their explanation of the fractional quantum Hall effect.
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 ...
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.
Haldane is known for a wide variety of fundamental contributions to condensed matter physics including the theory of Luttinger liquids, the theory of one-dimensional spin chains, the theory of fractional quantum hall effect, exclusion statistics, entanglement spectra and much more. [11] [12]