SKYRMIONS AND THE CROSSOVER FROM THE INTEGER TO FRACTIONAL QUANTUM HALL-EFFECT AT SMALL ZEEMAN ENERGIES

We study the two-dimensional electron gas in a high magnetic field at filling factor nu = 1 for an arbitrary ratio of the Zeeman energy gmu(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 g(c) 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 g(c), so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to nu = 1/3 and 1/5, is discussed.