Quantum Hall Skyrmions and Edge Spin Textures

Abstract: In the quantum Hall effect, new and surprising phenomena continue to be uncovered. For example, in quantum Hall ferromagnets Skyrmions have been observed---these quasiparticles carry electric charge and a large spin. The spin is ordered in a beautiful wavelike pattern, as shown on the front of this thesis. Another interesting aspect of quantum Hall systems is the structure of the edge. Skyrmions and phase transitions at the edges are the subjects of this thesis.At ferromagnetic filling factors a phase transition into a spin textured edge is proposed. In the textured phase, the spin is ordered in a Skyrmion like configuration. This is predicted to occur at small Zeeman energies when the confining potential at the edge softens. Tunneling of spin polarized particles into the edge might be used to experimentally detect the new phase. The phase transition is associated with a new edge mode, the edge spin wave mode. Various aspects of Skyrmions are also discussed, in particular the possibility to have a transition from charge one Skyrmions to charge two Skyrmions as the Zeeman energy is decreased.The calculations are performed using both a microscopic and an effective theory. These are compared in detail and found to be in good agreement with each other.