Skyrmions in quantum Hall systems

This thesis studies skyrmions in the SU(4) quantum Hall ferromagnet. Skyrmions are localized textures in ferromagnetic systems. The graphene monolayer in a strong magnetic field can be viewed as a ferromagnet with electron spin and Dirac-valley pseudo-spin - Landau levels with different spin and valley are close in energy and form to well-separated groups. Within one group, the Coulomb interaction has a manifest SU(4)-invariant form. The model of skyrmions used in this thesis is a classical, static field theory obtained from the variational principle. The model has phenomenological parameters, which depend on substrates and other experimental settings. Based on symmetry analysis, I propose the approach for skyrmions at quarter-filling and half-filling of the N = 0 Landau level in graphene monolayer. Energy minimization of single skyrmions is then performed to determine the parameters in the skyrmion approach, resulting in different types of spin-valley skyrmions at both filling factors. Large skyrmions are identified in certain ranges of the phenomenological parameters, where the ferromagnetic background of the skyrmion undergoes a phase transition. Single-mode spin-valley waves are also analyzed to characterize the SU(4) quantum Hall ferromagnet. A particular example shows instability of the ferromagnetic ground state. (author)