Charged Skyrmions: A condensate of spin excitons in a two-dimensional electron gas

The existence of topological defects, known as Skyrmions, within the spin-exciton energy band of a two-dimensional (2D) electron gas under a strong magnetic field at filling factor ν=1, is investigated within the Hartree-Fock (HF) approximation. Using the linear momentum representation, developed previously for the description of magnetoexcitons in 2D electron systems, it is shown that the inhomogeneity created in the system by a charged Skyrmion can be described by a nonuniform rotation of the spin-density operators in a condensate of spin excitons. In the limit when the spatial dependence of the rotation angles is very smooth on the magnetic length scale, it is found that the winding number of a created Skyrmion is equal to the number of particles injected to, or removed from the system. The minimum HF energy level of a neutral topological defect, i.e., a widely separated Skyrmion-anti-Skyrmion pair with a unit winding number, is found to lay exactly in the middle of the spin-exciton energy band.