Goldstone Mode Induced by Skyrmions in Quantum Hall Systems

Abstract

The properties of two-dimensional electron system exhibit rich physics in the presence of strong magnetic field. Electron-electron interactions add more interesting many-body phenomena to the systems, such as the frractional quantum Hall effect. From field theory method [1,2], a new type of topological excitation, Skyrmion, is predicted to occur around filling factor, 1/m, with odd integer m. The optically pumped nuclear magnetic resonance (OPNMR) measurements [3] support the existence of Skyrmions or spin texture excitations. Recently the present author has proposed that in quasi-2 + 1 dimensional quantum antiferromagnet the doped hole induces magnetic-disordered hedgehog-like soliton, which is composed of the doped hole and the cloud of SU(2) Yang-Mills fields with the spin disorder around the hole, by using the gauge-invariant effective Lagrangian with spontaneous symmetry breaking [4-7]. In this study, extending the theoretical formula, we introduce the gaugeinvariant effective Lagrangian density for the skyrmions around the filling factor = 1, and present the massless gauge field (Goldstone mode) induced by the Skyrmion. The massless gauge field introduces the long-range interaction, which will play an important role in the Skyrme crystal [8]. In addition, we suggest the presence of the skyrmion glass.