### Abstract

We study the two-dimensional electron gas in a high magnetic field at filling factor ν=1 for an arbitrary ratio of the Zeeman energy gμBB to the typical interaction energy. We find that the system always has a gap, even when the one-particle gap vanishes, i.e., when g=0. When g is sufficiently large, the quasiparticles are perturbatively related to those in the noninteracting limit; we compute their energies to second order in the Coulomb interaction. For g smaller than a critical value gc the quasiparticles change character; in the limit of g→0, they are skyrmions-spatially unbounded objects with infinite spin. In GaAs heterojunctions, the gap is unambiguously predominantly due to correlation effects; indeed, we tentatively conclude that g is always smaller than gc, so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to ν=1/3 and 1/5, is discussed.

Original language | English (US) |
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Pages (from-to) | 16419-16426 |

Number of pages | 8 |

Journal | Physical Review B |

Volume | 47 |

Issue number | 24 |

DOIs | |

State | Published - Jan 1 1993 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

*47*(24), 16419-16426. https://doi.org/10.1103/PhysRevB.47.16419