Fractional Quantum Hall Effect

:''

u = p/q

'',

where p and q are integers with no common factors. Here ''q'' always turns out to be an odd number. The principal series of such fractions are

:

{1\over 3}, {2\over 5}, {3\over 7}

etc.,

and

:

{2\over3}, {3\over 5}, {4\over 7}

, etc.

There are two main theories of the FQHE.

Fractionally-charged quasiparticles: this theory, proposed by Laughlin , hides the interactions by constructing a set of quasiparticles with charge $e^---={e\over q}$ , where the fraction is ${p\over q}$ as above.

Composite Fermions: this theory was proposed by Jain, and Halperin, Lee and Read. In order to hide the interactions, it attaches two (or, in general, an even number) flux quanta ${h\over e}$ to each electron, forming integer-charged quasiparticles called composite fermions. The fractional states are mapped to the integer QHE . This makes electrons at a filling factor 1/3, for example, behave in the same way as at filing factor 1. A remarkable result is that filling factor 1/2 corresponds to zero magnetic field. Experiments support this.

The importance of the FQHE was recognised in 1998 by the award of the Nobel Prize for Physics to Tsui, Störmer and Laughlin.

REFERENCES

[http://www.sp.phy.cam.ac.uk/SPWeb/research/FQHE.html University of Cambridge, Semiconductor Physics Group Research].

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Fractional Quantum Hall Effect