Skyrmions in arbitrarily polarized quantum Hall states

We derive an effective non-linear sigma model for quantum hall systems with arbitrary polarizations, by employing the recently proposed doublet model. We study the topological excitations, in particular, the skyrmions, as a function of the filling fraction as well as the polarization. We determine the relationship between the topological charge density and the electronic charge density, and the statistics of skyrmions. We also estimate the value of spin stiffness by using the dispersion relations that we have obtained recently by employing the time dependent Hartree-Fock approximation for the doublet model. Finally, we point out how the skyrmionic excitations reveal information directly on the number of flux tubes that get attached to the electrons in order to form composite fermions.