Skyrmions in the quantum hall effect

Abstract

The lowest energy charged excitations of the filling factor ν=1 quantum Hall ferromagnet are Skyrmions. The net spin of the Skyrmion’s is always larger than 1/2, in such a way that adding or removing charge from a Hall ferromagnet rapidly degrades its spin polarization. In the ground state of a two-dimensional electron gas at Landau level filling factor ν near 1 a finite density of Skyrmions could exits. In that case and for Zeeman coupling different from zero, the ground state is a Skyrme crystal with both spontaneous long range order in the charge density and spontaneous long range order in the transverse spin density. The energy of the Skyrme crystal is lowest for a square lattice structure with opposing postures for topological excitations on opposite sublattices. We discuss interpretations of our results in terms of non-linear σ and generalized spin models for quantum Hall ferromagnets. In the zero Zeeman coupling case, we find that the ground state can be interpreted as a meron crystal with two interpenetrating sublattices, each supporting quasiparticles with charge e/2.