Skyrmions and edge-spin excitations in quantum Hall droplets

We present a microscopic analysis of spin textures in quantum Hall droplets for filling factors v similar or equal to 1. We obtain analytical many-body wave functions of spin excitations which describe all of the necessary quantum numbers. An adequate linear combination of these eigenstates leads to wave functions in which the spatially dependent spinor can be factorized. This displays the topological structure of several spin textures, some of which are located at the bulk, and others at the edge. For the former, we obtain bulk charged skyrmions thai can be expressed as a condensate of spin excitons interacting via a two-body repulsive interaction. The size of the skyrmion is given by the number of excitons present in the condensate. We also obtain the skyrmion energy as a function of its size for both zero and finite Zeeman energy. For the edge excitations we find that a branch of these spin textures starts with lower energy than the branch of polarized charge edge excitations. When the number of electrons is of the order of a few tenths, there are no crossings of the spin and charge branches so that edge-spin textures can be responsible for the edge reconstruction of the droplet. On the contrary, edge reconstruction is always found to be due to polarized charge excitations when the number of electrons is larger than one hundred.