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Theoretical Study of the Quantum Hall Effect in Systems with Finite Width.

有限宽度系统中量子霍尔效应的理论研究。

基本信息

批准号：
63540281
负责人：
ONO Yoshiyuki
金额：
$ 1.09万
依托单位：
Toho University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540281/
关键词：
Quantum Hall Effect Edge States Anderson Localization Mesoscopic Systems Conductivity Fluctuations Fractal Dimension Inverse Participation Number Two Dimensional Electron System メゾスコッピック系逆参与数(Inverse Participation Number)2次元電子系量子ホール効

项目摘要

In order to investigate the effect of the finite system size we studied the electronic states and the current distribution in two dimensional disordered electron systems subject to perpendicular strong magnetic fields, by using computer simulations. The main results obtained in this study are as follows.1. There exist continuous transition between the bulk extended states and the edge states. When the bulk and edge states belonging to different Landau subbands are energetically degenerate, their hybridization occurs and its extent depends on the correlation length of impurity potentials.2. The delocalized states have a fractal character and extend with fractal dimensions smaller than two. As the energy decreases from the edge state region to the bulk region, the fractal dimensions vary from the anisotropic to the isotropic one.3. The sum rule about the center of mass of eigenstates, which is intimately related to the quantization of the Hall conductivity, has been confirmed numerically.4. The compensation of the Hall current has been found to be realized not only globally but also locally. Therefore, in the plateau region of the Hall conductivity, the Hall current distribution becomes uniform even in the disordered systems.5. In the region where the Hall conductivity as a function of the filling factor rises up, it shows large fluctuations and we have found large spatial fluctuations in the Hall current distribution.6. It has been found that the current control by the gate barrier is a quite useful technique in studying the current distribution inside the system not only experimentally but also theoretically.The inclusion of the Coulomb interaction has been found to reduce the apparent size effect on the Hall conductivity to some extent. However we could not succeed to clarity the theoretical limit of the accuracy of the Hall conductivity quantization.

为了研究有限系统尺寸的影响，我们通过计算机模拟研究了垂直强磁场作用下二维无序电子系统中的电子态和电流分布。本研究取得的主要结果如下： 1．体扩展态和边缘态之间存在连续的转变。当属于不同Landau子带的体态和边缘态进行能量简并时，它们会发生杂化，其程度取决于杂质势的相关长度。 2．离域态具有分形特征并以小于二的分形维数延伸。随着能量从边缘态区到体态区减小，分形维数从各向异性变为各向同性。 3．与霍尔电导率的量子化密切相关的本征态质心求和法则已得到数值证实。 4．霍尔电流的补偿不仅可以实现全局补偿，还可以实现局部补偿。因此，在霍尔电导率的平台区域，即使在无序系统中，霍尔电流分布也变得均匀。5．在霍尔电导率随填充因子上升的区域中，它表现出较大的波动，我们发现霍尔电流分布存在较大的空间波动。6．人们发现，通过栅极势垒控制电流是一种非常有用的技术，无论是在实验上还是在理论上研究系统内部的电流分布。库仑相互作用的加入可以在一定程度上减少霍尔电导率的表观尺寸效应。然而，我们无法成功阐明霍尔电导率量子化精度的理论极限。