Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies

Abstract

We study the two-dimensional electron gas in a high magnetic field at filling factor \ensuremath{\nu}=1 for an arbitrary ratio of the Zeeman energy g${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$B 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 ${\mathit{g}}_{\mathit{c}}$ the quasiparticles change character; in the limit of g\ensuremath{\rightarrow}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 ${\mathit{g}}_{\mathit{c}}$, so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to \ensuremath{\nu}=1/3 and 1/5, is discussed.