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Applications of gauge theories to low-dimensional electron systems

规范理论在低维电子系统中的应用

基本信息

批准号：
10640265
负责人：
SHIZUYA Ken-ichi
金额：
$ 1.86万
依托单位：
KYOTO UNIVERSITYKYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2001
项目状态：
已结题

项目摘要

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.

现在人们普遍认为规范场在凝聚态物理学和粒子物理学中发挥着重要作用。特别是，从量子霍尔系统中斯格明子激发的观察来看，低维电子系统为测试和应用规范理论的各种思想提供了一个良好且实用的场所。我们在过去四年的资助下，利用规范理论研究了有关量子霍尔效应基础的一些问题。 1．霍尔电流分布：霍尔样品中的电流分布是一个非常重要的主题。我们之前指出，由于从局部主导的样品内部排出，相当一部分霍尔电流将沿着样品边缘流动。我们进行了数值实验来验证体边缘霍尔电流的图像。2．量子霍尔效应的击穿：通过进一步的数值分析检验了上述数值实验提出的量子霍尔效应击穿的机制。指出观察到的击穿现象可能是由朗道能级内过程、无序与霍尔场之间的竞争来解释的。 3．分数量子霍尔效应 (FQHE)：开发了一种 FQHE 有效理论的新方法，该方法利用朗道能级和玻色化的投影，并依赖于量子霍尔态的不可压缩性质，而不参考标准复合玻色子或复合费米子图。特别是，对于双层系统，我们成功地构建了一种有效的规范理论，该理论正确地结合了集体激发谱，这是从一般磁转子理论中已知的，但传统的陈-西蒙斯理论无法实现。