quantum Hall effect

Regular steps in the Hall conductivity effect at low temperatures in high magnetic fields for electrons constrained to move in a plane, such as in the junction region of silicon-metal oxide semiconductor devices; first observed in 1980 by Klaus von Klitzing and others; sometimes termed the integer quantum Hall effect. It results from the quantized orbiting motion of electrons in a magnetic field. The conductivity has values that are integer multiples of e²/h, where e is the electron charge and h is Planck's constant. In 1982 Horst Störmer and Daniel Tsui discovered the fractional Hall effect, in which the conductivity has certain fractional multiples of e²/h. This result was explained by Robert Laughlin as due to a new type of quasi-particle formed from electrons and microscopic magnetic whirlpools. These quasi-particles form a ‘quantum fluid’ with parallels in liquid helium and superconductors. Störmer, Tsui, and Laughlin were awarded the 1998 Nobel Prize for Physics.

The 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 takes on the quantized values

where e is the elementary charge and h is Planck's constant. In the "ordinary" quantum Hall effect, known as the integer quantum Hall effect, ν takes on integer values (ν = 1, 2, 3, etc.). There is another type of quantum Hall effect, known as the fractional quantum Hall effect, in which ν can occur as a vulgar fraction (ν = 2/7, 1/3, 2/5, 3/5, 5/2 etc.)

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 e²/h to nearly one part in a billion. 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 integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation. It was only in 1980 that von Klitzing, working with samples developed by Michael Pepper and Gerhard Dorda, made the totally unexpected discovery that the Hall conductivity was exactly quantized.

The fractional effect is due to completely different physics, and was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard. Although it was generally assumed that the discrete resistivity jumps found in the Tsui experiment were due to the presence of fractional charges (i.e., due to the emergence of quasiparticles with charges smaller than an electron charge), it was not until 1997 that R. The fractional quantum Hall effect continues to be influential in theories about topological order.