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quantum hall effect
The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance ''σ'' undergoes certain quantum Hall transitions to take on the quantized values
:
where is the channel current, is the Hall voltage, ''e'' is the elementary charge and ''h'' is Planck's constant. The prefactor ''ν'' is known as the "filling factor", and can take on either integer (''ν'' = 1, 2, 3, ...) or fractional (''ν'' = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5, ...) values. 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 integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see Landau quantization). The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions. Although the microscopic origins of the fractional quantum Hall effect are unknown, there are several phenomenological approaches that provide accurate approximations. For example the effect can be thought of as an integer quantum Hall effect, not of electrons but of charge-flux composites known as composite fermions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.
==Applications==
The quantization of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of ''e''2/''h'' to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of gauge invariance. It has allowed for the definition of a new practical standard for electrical resistance, based on the resistance quantum given by the von Klitzing constant ''R''K = ''h''/''e''2 = 25812.807557(18) Ω. This is named after Klaus von Klitzing, the discoverer of exact quantization. Since 1990, a fixed conventional value ''R''K-90 is used in resistance calibrations worldwide.〔(【引用サイトリンク】title= conventional value of von Klitzing constant )〕 The quantum Hall effect also provides an extremely precise independent determination of the fine structure constant, a quantity of fundamental importance in quantum electrodynamics.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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