Skyrmions in arbitrarily polarized quantum Hall states

TL;DR

This paper develops an effective non-linear sigma model for quantum Hall systems with arbitrary polarization, analyzing skyrmion excitations, their properties, and implications for composite fermion formation.

Contribution

It introduces a novel sigma model approach for polarized quantum Hall states and explores skyrmion characteristics and their relation to electron flux attachment.

Findings

Derived the relationship between topological charge density and electronic charge density.

Estimated spin stiffness using dispersion relations from time-dependent Hartree-Fock.

Showed how skyrmions encode information about flux tubes in composite fermions.

Abstract

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.