Skyrmion excitations in quantum Hall systems

[摘要] Using finite-size calculations on the surface of a sphere we study the topological (Skyrmion) excitation in quantum Hall systems with spin degrees of freedom at filling factors around nu=1. In the absence of Zeeman energy, we find, in systems with one quasiparticle or one quasihole, the lowest-energy band consists of states with L=S, when L and S are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one Skyrmion of infinite size. In the presence of Zeeman energy, the Skyrmion size is determined by the interplay of the Zeeman energy and the electron-electron interaction and the Skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave-vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the Skyrmion.

[关键词] ELECTRON-SYSTEMS;MAGNETIC-FIELD;SPIN;STATES