### 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 language | English (US) |
---|---|

Pages (from-to) | 105-146 |

Number of pages | 42 |

Journal | Advances in Physics |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1992 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

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*Advances in Physics*, vol. 41, no. 2, pp. 105-146. https://doi.org/10.1080/00018739200101483

**Microscopic theory of the fractional quantum Hall effect.** / Jain, Jainendra K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Microscopic theory of the fractional quantum Hall effect

AU - Jain, Jainendra K.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

AB - 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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U2 - 10.1080/00018739200101483

DO - 10.1080/00018739200101483

M3 - Article

AN - SCOPUS:2842591475

VL - 41

SP - 105

EP - 146

JO - Advances in Physics

JF - Advances in Physics

SN - 0001-8732

IS - 2

ER -