Microscopic theory of the fractional quantum Hall effect

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Abstract

This is a review of the composite fermion theory of the fractional quantum Hall effect (FQHE). This theory provides a microscopic description of the low energy states of the strongly correlated electrons in the FQHE regime in terms of weakly interacting composite fermions, where a composite fermion is an electron bound to an even number of vortices. In the simplest cases, the FQHE can be construed as a manifestation of the integer quantum Hall effect of the composite fermions. Based on these ideas, simple Jastrow-Slater trial wavefunctions are written for the incompressible FQHE states as well as their low energy excitations. Extensive numerical work has been performed to confirm their validity. In particular, these have essentially 100% overlap with the true Coulomb states for few particle systems. Various consequences of the theory are in excellent agreement with experiments. Notably, it provides a unified framework for the fractional and integer quantum Hall effects, consistent with the experimental fact that there is no qualitative distinction between the observation of various plateaus. Also, the prominent fractions are clearly identified and compare well with the experimentally observed fractions.

Original languageEnglish (US)
Pages (from-to)105-146
Number of pages42
JournalAdvances in Physics
Volume41
Issue number2
DOIs
StatePublished - Jan 1 1992

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Quantum Hall effect
quantum Hall effect
Fermions
fermions
composite materials
Composite materials
integers
Electrons
Excitation energy
Wave functions
Electron energy levels
plateaus
Vortex flow
electrons
vortices
energy
excitation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

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abstract = "This is a review of the composite fermion theory of the fractional quantum Hall effect (FQHE). This theory provides a microscopic description of the low energy states of the strongly correlated electrons in the FQHE regime in terms of weakly interacting composite fermions, where a composite fermion is an electron bound to an even number of vortices. In the simplest cases, the FQHE can be construed as a manifestation of the integer quantum Hall effect of the composite fermions. Based on these ideas, simple Jastrow-Slater trial wavefunctions are written for the incompressible FQHE states as well as their low energy excitations. Extensive numerical work has been performed to confirm their validity. In particular, these have essentially 100{\%} overlap with the true Coulomb states for few particle systems. Various consequences of the theory are in excellent agreement with experiments. Notably, it provides a unified framework for the fractional and integer quantum Hall effects, consistent with the experimental fact that there is no qualitative distinction between the observation of various plateaus. Also, the prominent fractions are clearly identified and compare well with the experimentally observed fractions.",
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Microscopic theory of the fractional quantum Hall effect. / Jain, Jainendra K.

In: Advances in Physics, Vol. 41, No. 2, 01.01.1992, p. 105-146.

Research output: Contribution to journalArticle

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