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

摘要

A microscopic description of (baby)skyrmions in quantum Hall ferromagnets isderived from a scattering theory of collective (neutral) spin modes by a barequasiparticle. We start by mapping the low lying spectrum of spin waves in theuniform ferromagnet onto that of free moving spin excitons, and then we studytheir scattering by the defect of charge. In the presence of this disturbance,the local spin stiffness varies in space, and we translate it into aninhomogeneus metric in the Hilbert space supporting the excitons. An attractivepotencial is then required to preserve the symmetry under global spinrotations, and it traps the excitons around the charged defect. Thequasiparticle now carries a spin texture. Textures containing more than oneexciton are described within a mean-field theory, the interaction among theexcitons being taken into account through a new renormalization of the metric.The number of excitons actually bound depends on the Zeeman coupling, thatplays the same role as a chemical potencial. For small Zeeman energies, thedefect binds many excitons which condensate. As the bound excitons have a unitof angular momentum, provided by the quantum of magnetic flux left unbalancedby the defect of charge, the resulting texture turns out to be a topologicalexcitation of charge 1. Its energy is that given by the non-linear sigma modelfor the ground state in this topological sector, i.e. the texture is askyrmion.