Fractional quantum Hall effect. Scheme, description

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Fractional quantum Hall effect. Encyclopedia of radio electronics and electrical engineering

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Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur

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A lot has been written about the Hall effect, this effect is intensively used in technology, but scientists continue to study it. In 1980, the German physicist Klaus von Klitzung studied the operation of the Hall effect at ultralow temperatures. In a thin semiconductor plate, von Klitzung smoothly changed the strength of the magnetic field and found that the Hall resistance does not change smoothly, but jumps. The magnitude of the jump did not depend on the properties of the material, but was a combination of fundamental physical constants divided by a constant number. It turned out that the laws of quantum mechanics somehow changed the nature of the Hall effect. This phenomenon has been called the integral quantum Hall effect. For this discovery, von Klitzung received the Nobel Prize in Physics in 1985.

Two years after von Klitzung's discovery at Bell Telephone's lab (the same one where the transistor was discovered), Stormer and Tsui were studying the quantum Hall effect using an exceptionally pure, large sample of gallium arsenide made at the same lab. The sample had such a high degree of purity that the electrons passed from end to end without encountering obstacles. Stormer and Tsui's experiment took place at a much lower temperature (almost absolute zero) and with stronger magnetic fields than von Klitzung's experiment (a million times stronger than the Earth's magnetic field).

Much to their surprise, Stormer and Tsui found a jump in Hall's resistance three times that of von Klitzung's. Then they found even bigger jumps. The same combination of physical constants was obtained, but divided not by an integer, but by a fractional number. The charge of an electron is considered by physicists to be a constant, not divisible by parts. And in this experiment, as it were, particles with fractional charges participated. The effect was called the fractional quantum Hall effect.

A year after this discovery, Laughlin, a laboratory employee, gave a theoretical explanation of the effect. He stated that the combination of ultra-low temperature and a powerful magnetic field causes the electrons to form an incompressible quantum fluid. The figure shows the flow of electrons (balls) piercing the plane using computer graphics. The irregularities of the plane represent the distribution of the charge of one of the electrons in the presence of a magnetic field and the charge of other electrons.

If an electron is added to a quantum liquid, then a certain amount of quasiparticles with a fractional charge is formed (in the figure, this is shown as a set of arrows for each electron).

Fractional quantum Hall effect

In 1998, Horst Stormer, Daniel Tsui and Robert Laughlin were awarded the Nobel Prize in Physics. Currently, H. Stormer is a professor of physics at Columbia University, D. Tsui is a professor at Princeton University, and R. Laughlin is a professor at Stanford University.

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