### Abstract

A theoretical framework is presented which provides a unified description of the integer and the fractional quantum Hall effects. The main assertion is that new candidate incompressible states can be constructed by taking products of some known incompressible states, and all incompressible states can thus be generated starting from the states at integer filling factors. The crucial difference from previous theories is that the higher Landau levels play an essential role in identifying the correlations responsible for the fractional quantum Hall effect. The quasiparticle excitations of the fractional states can be understood simply in this approach by analogy to the quasiparticles of the integer states. Numerical results show that these trial states very accurately describe the transition from the 1/3 state to the 2/5 state for a four-electron system. It is further shown that the predictions of the theory are completely consistent with the phenomenology of the fractional quantum Hall effect; in particular, the predicted order of stability of the various fractions is in agreement with experiments. Even though the fractional quantum Hall effect is found to be possible at all rational filling factors in this approach, it is indicated why the odd-denominator fractions are in general more stable than the even-denominator ones.

Original language | English (US) |
---|---|

Pages (from-to) | 7653-7665 |

Number of pages | 13 |

Journal | Physical Review B |

Volume | 41 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1990 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*41*(11), 7653-7665. https://doi.org/10.1103/PhysRevB.41.7653

}

*Physical Review B*, vol. 41, no. 11, pp. 7653-7665. https://doi.org/10.1103/PhysRevB.41.7653

**Theory of the fractional quantum Hall effect.** / Jain, J. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Theory of the fractional quantum Hall effect

AU - Jain, J. K.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - A theoretical framework is presented which provides a unified description of the integer and the fractional quantum Hall effects. The main assertion is that new candidate incompressible states can be constructed by taking products of some known incompressible states, and all incompressible states can thus be generated starting from the states at integer filling factors. The crucial difference from previous theories is that the higher Landau levels play an essential role in identifying the correlations responsible for the fractional quantum Hall effect. The quasiparticle excitations of the fractional states can be understood simply in this approach by analogy to the quasiparticles of the integer states. Numerical results show that these trial states very accurately describe the transition from the 1/3 state to the 2/5 state for a four-electron system. It is further shown that the predictions of the theory are completely consistent with the phenomenology of the fractional quantum Hall effect; in particular, the predicted order of stability of the various fractions is in agreement with experiments. Even though the fractional quantum Hall effect is found to be possible at all rational filling factors in this approach, it is indicated why the odd-denominator fractions are in general more stable than the even-denominator ones.

AB - A theoretical framework is presented which provides a unified description of the integer and the fractional quantum Hall effects. The main assertion is that new candidate incompressible states can be constructed by taking products of some known incompressible states, and all incompressible states can thus be generated starting from the states at integer filling factors. The crucial difference from previous theories is that the higher Landau levels play an essential role in identifying the correlations responsible for the fractional quantum Hall effect. The quasiparticle excitations of the fractional states can be understood simply in this approach by analogy to the quasiparticles of the integer states. Numerical results show that these trial states very accurately describe the transition from the 1/3 state to the 2/5 state for a four-electron system. It is further shown that the predictions of the theory are completely consistent with the phenomenology of the fractional quantum Hall effect; in particular, the predicted order of stability of the various fractions is in agreement with experiments. Even though the fractional quantum Hall effect is found to be possible at all rational filling factors in this approach, it is indicated why the odd-denominator fractions are in general more stable than the even-denominator ones.

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UR - http://www.scopus.com/inward/citedby.url?scp=11744298055&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.41.7653

DO - 10.1103/PhysRevB.41.7653

M3 - Article

AN - SCOPUS:11744298055

VL - 41

SP - 7653

EP - 7665

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 11

ER -