|
The quantum Hall effect (QHE) is the quantization of the Hall resistance, which may be
observed in the presence of large magnetic field strength and low
temperature. It was discovered in 1980
by Klaus von Klitzing, Michael Pepper, and Gerhard Dorda.
In a typical QHE experiment, a MOSFET is subjected to a large magnetic field of
order 15 T, at a temperature of order 1 K.
There is a two-dimensional electron gas maintained in the inversion layer of the
MOSFET, the plane of which is aligned perpendicular to the magnetic field. When an electric field is applied in the plane, the
corresponding Hall resistance is found to be quantized in units of
- RH = h / (e2 n)
where h is Planck's constant, e the
elementary charge, and n an integer. This is referred to as the
Integer Quantum Hall Effect (IQHE).
In 1982, Daniel Tsui and Horst Stormer discovered the Fractional Quantum Hall Effect. Working at lower
temperatures and stronger magnetic fields, they found a Hall resistance quantized in units of 3h /
e2, i.e. n = 1/3. Other fractional quantizations - for example, 2/5, 3/5, and 2/7 - were
subsequently found. The FQHE was explained in 1983 by Robert Laughlin, using a many-body wavefunction that has a lower energy than the single-particle energy. In the Fractional
Quantum Hall Effect, the quasiparticle charge is less than the
electron charge. The fractionally charged quasiparticles were observed in 1997.
The quantum Hall effect provides an invariable standard of resistance based on fundamental constants. In 1990, the
International System of Units (SI) redefined the Ohm in
terms of the QHE, with the accepted value of the quantum Hall resistance (or von Klitzing constant, after the
effect's discoverer). The quantum Hall effect was also used as an independent determination of the fine structure constant in quantum electrodynamics.
References
- K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
- D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)
- R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
|