The fractional quantum Hall effect

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The fractional quantum Hall effect (FQHE) is a fascinating manifestation of simple collective behaviour in a two-dimensional system of strongly interacting electrons. At particular magnetic fields, the electron gas condenses into a remakable state with liquid-like properties. This state is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. As in the integer Quantum Hall Effect, a series of plateaux forms in the Hall resistance. Each particular values of magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) nu=p/q, where p and q are integers with no common factors). q always turns out to be an odd number. The principal series of such fractions are 1/3, 2/5, 3/7 etc, and 2/3, 3/5, 4/7, 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/q, where the fraction is p/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/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, Stormer and Laughlin, see this Nobel prize web site for more information.

Some of our research on the FQHE:

• Antidots
• Non-equilibrium transport in edge states