THEORETICAL INVESTIGAYTION OF QUANTUM HALL EFFECT

量子霍尔效应的理论研究

基本信息

批准号：
07640522
负责人：
ISHIKAWA Kenzo
金额：
$ 1.41万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640522/
关键词：
Quantum Hall effect fractional Hall effect von Neumann lattice flux phase Hofstadter butterfly duality topological field theory quantum field theory von Neumann格子表現有限サイズ補正抵抗標準

项目摘要

Various problems of Quantum Hall effect are studied based on field theory that is formulated using von Neumann lattice representation and the following new results have been obtained.1. Integer Quantum Hall effectInteger quantum Hall effect is used for standard of resistance and for determining the fine strusture constant. Concerning finite size effect and finite current effect, it was shown in this project that under sufficently strong magnetic field, corrections vanish and the Hall conductance is quantized exactly in realistic two-dimensional systems. The quantum Hall effect disappears, however, if thhe current exceeds a critical value. The critical Hall field is proportional to two halvth of the magnetic field.2. Fractional Hall effectA new mean field theory of the fractional Hall effect based on flux condenced state on von Neumann lattice is proposed. In this theory, one particle spectrum has a fractal structure owing to two scales of the system, lattice constant and flux per plaquette. The latter is connected with the filling factor. It is shown, for the first time, that the fractional Hall effect is understood from Hofstadter butterfly.3. Periodic potentials in the strong magnetic field and dualityOne particle spectra of the systems with periodic short range potentials are obtained by using von Neumann lattice representation. A kind of duality relation is shown to be hold.4. A symmetry breaking of topological field theory by Gribov copies is analyzed.

基于冯·诺依曼晶格表示形式的场论研究了量子霍尔效应的各种问题，取得了以下新成果： 1．整数量子霍尔效应整数量子霍尔效应用于电阻标准和确定精细结构常数。关于有限尺寸效应和有限电流效应，该项目表明，在足够强的磁场下，修正消失，霍尔电导在现实的二维系统中被精确量化。然而，如果电流超过临界值，量子霍尔效应就会消失。临界霍尔场与磁场的二分之一成正比。2．分数霍尔效应提出了一种基于冯诺依曼晶格通量凝聚态的分数霍尔效应新平均场理论。在这一理论中，由于系统的两个尺度、晶格常数和每块通量，一个粒子光谱具有分形结构。后者与填充因子有关。首次表明，从Hofstadter蝴蝶中理解了分数霍尔效应。 3．利用冯·诺依曼晶格表示，获得了强磁场中的周期势和对偶性短程势周期系统的粒子谱。证明了一类对偶关系成立。 4．分析了 Gribov 副本对拓扑场论的对称性破缺。