Applications of gauge theories to low-dimensional electron systems

点击翻译按钮获取中文摘要

It is now widely accepted that gauge fields play an important role in condensed-matter physics as well as in particle physics. In particular, as seen from the observation of Skyrmion excitations in quantum Hall systems, low-dimensional electron systems offer a good and practical place to test and apply various ideas of gauge theories. Under a Grant-in-Aid over the past four years, we have thus studied some problems pertaining to the foundation of the quantum Hall effect by use of gauge theories.1. Hall-current distribution : The current distribution in a Hall sample is a subject of basic importance. We had earlier pointed out that a considerable portion of the Hall current would flow along the sample edges as a consequence of expulsion out of the localization-dominated sample interior. We carried out a numerical experiment to verify this picture of the bulk-edge Hall current.2. Breakdown of the quantum Hall effect : A mechanism for the breakdown of the quantum Hall effect, suggested from the above numerical experiment, was examined by a further numerical analysis. It was pointed out that the observed breakdown phenomena may be explained by an intra-Landau-level process, competition between disorder and the Hall field.3. Fractional quantum Hall effect (FQHE) : A new approach to the effective theory of the FQHE was developed, that makes use of projection to Landau levels and bosonization and that relies on the incompressible nature of the quantum Hall states without referring to the standard composite-boson or composite- fermion picture. In particular, for double-layer systems we succeeded in constructing an effective gauge theory that properly incorporates the collective-excitation spectrum, known from a general magneto-roton theory but inaccessible by the conventional Chern-Simons theories.