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 quantum Hall transitions to take on the quantized values 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 quantum Hall transitions to take on the quantized values where Ichannel is the channel current, VHall 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 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. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization). The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions. The fractional quantum Hall effect is also understood as an integer quantum Hall effect, although 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. The quantization of the Hall conductance has the important property of being exceedingly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e2/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 RK = h/e2 = 25812.807557(18) Ω. This is named after Klaus von Klitzing, the discoverer of exact quantization. Since 1990, a fixed conventional value RK-90 has been used in resistance calibrations worldwide. On 16 November 2018, the conventional value was abrogated in consequence of the decision to fix the values of h (the Planck constant) and e (the elementary charge) at the 26th meeting of the General Conference on Weights and Measures. The quantum Hall effect also provides an extremely precise independent determination of the fine-structure constant, a quantity of fundamental importance in quantum electrodynamics. The MOSFET (metal-oxide-semiconductor field-effect transistor), invented by Mohamed Atalla and Dawon Kahng at Bell Labs in 1959, enabled physicists to study electron behavior in a nearly ideal two-dimensional gas. In a MOSFET, conduction electrons travel in a thin surface layer, and a 'gate' voltage controls the number of charge carriers in this layer. This allows researchers to explore quantum effects by operating high-purity MOSFETs at liquid helium temperatures. The integer quantization of the Hall conductance was originally predicted by University of Tokyo researchers Tsuneya Ando, Yukio Matsumoto and Yasutada Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true. In 1978, the Gakushuin University researchers Jun-ichi Wakabayashi and Shinji Kawaji subsequently observed the effect in experiments carried out on the inversion layer of MOSFETs. In 1980, Klaus von Klitzing, working at the high magnetic field laboratory in Grenoble with silicon-based MOSFET samples developed by Michael Pepper and Gerhard Dorda, made the unexpected discovery that the Hall conductivity was exactly quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. The link between exact quantization and gauge invariance was subsequently found by Robert Laughlin, who connected the quantized conductivity to the quantized charge transport in Thouless charge pump. Most integer quantum Hall experiments are now performed on gallium arsenide heterostructures, although many other semiconductor materials can be used. In 2007, the integer quantum Hall effect was reported in graphene at temperatures as high as room temperature, and in the magnesium zinc oxide ZnO–MgxZn1−xO.