Fractional quantum Hall effect

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The fractional quantum Hall effect (FQHE) is a physical phenomenon in which a certain system behaves as if it were composed of particles with charge smaller than the elementary charge. Its discovery and explanation were recognized by the 1998 Nobel Prize in Physics.

Contents 1 Introduction 2 Other evidence for fractionally-charged quasiparticles 3 See also 4 References

[edit] Introduction

The fractional quantum Hall effect (FQHE) is a manifestation of simple collective behaviour in a two-dimensional system of strongly interacting electrons. At particular magnetic fields, the electron gas condenses into a remarkable 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 plateaus forms in the Hall resistance. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta)

ν = p / q,

where p and q are integers with no common factors. Here q turns out to be an odd number with the exception of two filling factors 5/2 and 7/2. The principal series of such fractions are

etc.,

and

, etc.

There were two major steps in the theory of the FQHE.

• Fractionally-charged quasiparticles: this theory, proposed by Laughlin, is based on accurate trial wave functions for the ground state at fraction 1 / q as well as its quasiparticle and quasihole excitations. The excitations have fractional charge of magnitude .

• Composite fermions: this theory was proposed by Jain, and Halperin, Lee and Read. As a result of the repulsive interactions, two (or, in general, an even number) flux quanta are captured by 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 composite fermion theory.

The FQHE was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work.

Laughlin's original plasma model was extended to other fractionally charged systems by MacDonald and others^[1]. An approach based on the idea of composite Fermions^[2] has now emerged as a basic paradigm encompassing most of the earlier approaches.

Fractionally charged quasiparticles are neither bosons nor fermions and exhibit anyonic statistics. The fractional quantum Hall effect continues to be influential in theories about topological order. Certain fractional quantum Hall phases appear to have the right properties for building a topological quantum computer.

[edit] Other evidence for fractionally-charged quasiparticles

Apart from the FQHE itself, further evidence has continued to emerge that specifically supports the understanding that there are fractionally-charged quasiparticles in an electron gas under FQHE conditions.

In 1995, the fractional charge of Laughlin quasiparticles was measured directly in a quantum antidot electrometer at Stony Brook University, New York.^[3] In 1997, two groups of physicists at the Weizmann Institute of Science in Rehovot, Israel, and at the Commissariat à l'énergie atomique laboratory near Paris, detected such quasiparticles carrying an electric current, through measuring quantum shot noise.^[4][5]

[edit] See also

• Laughlin wavefunction
• Hall probe

[edit] References

• University of Cambridge, Semiconductor Physics Group Research.
• D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982) doi:10.1103/PhysRevLett.48.1559
• R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983) doi:10.1103/PhysRevLett.50.1395

• Fractional quantum Hall effect( List of Authority Articles)