Theoretical Study of Two-Dimensional Electronic States in a Random Magnetic Field

随机磁场中二维电子态的理论研究

• 批准号: 10640321
• 负责人: YAKUBO Kousuke
• 金额: $ 2.3万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640321/
• 关键词: Random Magnetic Field; Localization; Finite-Size Scaling; Multifractal; Universality Class; Fractional Quantum Hall Effect; 強制振動子法; スーパー・コンピュータ; 大規模行列; 応答関数; 久保公式

In recent years there has been a growing interest in two-dimensional electrons in a random magnetic field. Instead of importance of the problem, there still exist many unsolved questions in this field. We have studies the localization property of two-dimensional electrons in random magnetic fields in terms of a novel finite-size scaling based on the multifractality of the critical wave function. At first, we have determined the existence of the metal-insulator transition in a system subject to a random magnetic field with vanishing mean and its universality class. The result suggests that all electronic states are localized in such systems. We also investigated systems in a random magnetic field with finite mean. In the case that the average field is much stronger than the magnitude of field fluctuations, the spectrum separates into Landau subbands and only the states at subband centers are extended as predicted by a semiclassical theory. We confirmed that the universality class of this transition is the same with that of the integer quantum Hall system. Furthermore, the energy of the extended state shifts upward from the subband center when the magnitude of field fluctuation becomes stronger. These results are quite important for understanding electron transport in a fractional quantum Hall system near v=1/2.

近年来，对随机磁场中的二维电子的兴趣越来越大。该领域仍然存在许多未解决的问题，而不是问题的重要性。我们研究了基于临界波函数的多重纹理，研究了二维电子在随机磁场中的定位特性。首先，我们确定了由具有消失平均值及其普遍性类别的随机磁场的系统中金属 - 绝缘体转变的存在。结果表明，所有电子状态都位于此类系统中。我们还研究了具有有限平均值的随机磁场中的系统。如果平均场比场波动的幅度强得多，则频谱分为Landau子带，并且只有子带中心处的状态可以按照半经典理论的预测进行扩展。我们证实，该过渡的通用类别与整数量子厅系统的通用类别相同。此外，当场波动的大小变得更强时，延伸状态的能量从子带中心向上移动。这些结果对于了解近乎v = 1/2的分数量子厅系统中的电子传输非常重要。

项目成果

K. Yakubo: "Transfer matrix method for a dynamical mesoscopic system"Physical Review E. 57-3. 3602-3610 (1998)

K. Yakubo：“动态介观系统的传递矩阵方法”物理评论 E. 57-3。

K.Yakubo: "Finite-size scaling of multifractal wave functions : The metal-insulator transition in two-dimensional symplectic systems"Physical Review B. 58(15). 9767-9772 (1998)

K.Yakubo：“多重分形波函数的有限尺寸缩放：二维辛系统中的金属-绝缘体转变”物理评论 B. 58(15)。

K. Yakubo and M. Ono: "Finite-size scaling of multifractal wave functions : The metal-insulator transition in two-dimensional symplectic systems"Physical Review B. 58-15. 9767-9772 (1998)

K. Yakubo 和 M. Ono：“多重分形波函数的有限尺寸缩放：二维辛系统中的金属-绝缘体转变”物理评论 B. 58-15。

K.Yakubo: "Transfer matrix method for a dynamical mesoscopic system" Physical Review E. 57. 3602-3610 (1998)

K.Yakubo：“动态介观系统的传递矩阵方法”物理评论 E. 57. 3602-3610 (1998)

K.Yakubo and M.Ono: "Finite-size scaling of multifractal wave functions : The metal-insulator transition in two-dimensional symplectic systems" Physical Review B. 58. 9767-9772 (1998)

K.Yakubo 和 M.Ono：“多重分形波函数的有限尺寸缩放：二维辛系统中的金属-绝缘体转变”物理评论 B. 58. 9767-9772 (1998)