Skyrmions in quantum Hall ferromagnets as spin-waves bound to unbalanced magnetic flux quanta

Abstract

A microscopic description of (baby)skyrmions in quantum Hall ferromagnets is derived from a scattering theory of collective (neutral) spin modes by a bare quasiparticle. We start by mapping the low lying spectrum of spin waves in the uniform ferromagnet onto that of free moving spin excitons, and then we study their scattering by the defect of charge. In the presence of this disturbance, the local spin stiffness varies in space, and we translate it into an inhomogeneus metric in the Hilbert space supporting the excitons. An attractive potencial is then required to preserve the symmetry under global spin rotations, and it traps the excitons around the charged defect. The quasiparticle now carries a spin texture. Textures containing more than one exciton are described within a mean-field theory, the interaction among the excitons being taken into account through a new renormalization of the metric. The number of excitons actually bound depends on the Zeeman coupling, that plays the same role as a chemical potencial. For small Zeeman energies, the defect binds many excitons which condensate. As the bound excitons have a unit of angular momentum, provided by the quantum of magnetic flux left unbalanced by the defect of charge, the resulting texture turns out to be a topological excitation of charge 1. Its energy is that given by the non-linear sigma model for the ground state in this topological sector, i.e. the texture is a skyrmion.