Mar 2, 2000
Fractional quantum Hall effects
The behaviour of two-dimensional electron gases in strong magnetic fields at low temperatures has been a rich source of new physics for two decades, and continues to surprise theorists and experimentalists alike.
Since its discovery almost two decades ago, the quantum Hall effect has been investigated by an exceptionally broad community of physicists, ranging all the way from materials scientists to topologists. Although the integer and fractional quantum Hall effects were discovered in the early 1980s, they are still the focus of a large research effort worldwide, and many new phenomena have been discovered in recent years. These include objects as diverse as composite fermions, skyrmions and fractional charge carriers.
The classical Hall effect, which dates back to the 19th century, is widely used to characterize electronic materials. In the classical effect, a thin strip of a conducting material is placed in a magnetic field and a current is driven through it. The electrons experience a Lorentz force that is perpendicular to both the magnetic field and their initial direction. If the electrons are initially moving in the x direction through a strip in the x-y plane and the magnetic field is in the z direction, then the Lorentz force, and hence the Hall voltage, will be in the y direction.
The quantum Hall effect violates the classical theory in a dramatic way. When the Hall effect is measured at low temperatures in a sample that is so thin that the electrons are confined to move only in the x-y plane, the Hall resistance is found to deviate from the classical behaviour. At sufficiently high fields, a series of flat "steps" appear in the graph of the Hall resistance versus magnetic field. This integer quantum Hall effect was discovered by Klaus von Klitzing, Michael Pepper and Gerhard Dorda in 1980. Two years later Daniel Tsui, Horst Störmer and Arthur Gossard discovered that these steps could take on fractional values to a precision close to one part in a billion, making the Hall effect one of the most precise phenomena known in physics.
In the March issue of Physics World magazine, Moty Heiblum and Ady Stern from the Weizmann Institute of Science, Rehovot, Israel report on the latest research with two-dimensional electron gases.
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