Anderson transitions in disordered systems and electron correlations

无序系统中的安德森跃迁和电子关联

• 批准号: 16540294
• 负责人: KAWARABAYASHI Tohru
• 金额: $ 2.05万
• 依托单位: Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540294/
• 关键词: Anderson localization; quantum Hall system; magneto transport; edge states; correlated random potential; random magnetic fields; 量子ホール細線; ランダウアー公式; ランダウ準位; 不純物散乱; シュブニコフ-ド・ハース効果; 量子ホール転移; 臨界コンダクタンスの分布; シュブニコフード・ハース効果; Anderson localization; quantum Hall system; magneto transport; edge states; correlated random potential; random magnetic fields; 量子ホール細線; ランダウアー公式; ランダウ準位; 不純物散乱; シュブニコフ-ド・ハース効果; 量子ホール転移; 臨界コンダクタンスの分布; シュブニコフード・ハース効果

In 2004 and 2005, we have studied the transport properties of the two-dimensional system in a disordered magnetic field with a fixed sign. This model corresponds to the case where the random fluctuation of the magnetic field is of the same order of its mean value. The two-dimensional random magnetic field system arises in the theory of the fractional quantum Hall system where the electron correlation plays an important role. It has then been found for systems without edge states that the conductance is insensitive to the strength of the fluctuation of the magnetic field and stays on the order of the conductance quantum in the limit of weak magnetic fields. This singular behavior can be understood within the framework of the Drude formula. Apart from this classical singularity in the weak field limit, we have also shown that the Shubnikov-de Haas effect is clearly seen in this system.We have also investigated the statistical properties of the conductance in such a system. In particular, … More the critical conductance distribution has been analyzed in detail. In the presence of edge states, it has been shown that the critical distribution of conductance exhibits a wide distribution whose width is of the order of the conductance quantum. For systems with no edge state, the critical distribution similar to that for the network model and that for the model with potential disorder has been obtained, suggesting the universality of the critical distribution.In 2006, we have studied the effect of potential correlation in quantum Hall wires and found unexpected feature introduced by the potential correlation. In real materials, the impurity potential has a finite potential range and thus the disorder potential has a finite correlation length. It is therefore important to consider the effect of potential correlation as well as the electron correlation. In the absence of impurities, the conductance of the quantum Hall wire exhibits the quantized steps at the bulk Landau levels. In the presence of impurities, the impurity scattering mixes the edge states with the bulk states and the conductance becomes exponentially small at the conductance plateau transitions. We have found that when the potential correlation length is larger than the magnetic length, the small conductance region disappears as expected. Apart from it, we have also found unexpectedly that the conductance steps shift toward higher energies. This new feature is specific to long wires. We have argued semi-classically that the shift is a consequence of the reflection of edge states due to smoothly varying disorder potential. Less

在2004年和2005年，我们研究了带有固定符号的无序磁场中二维系统的运输特性。该模型对应于磁场的随机波动的平均值相同顺序。二维随机磁场系统出现在分数量子厅系统的理论中，其中电子相关起着重要作用。随后，没有边缘状态的系统发现电导对磁场波动的强度不敏感，并且在弱磁场极限下保持在电导量子的顺序。可以在Drude公式的框架内理解这种奇异行为。除了在弱场限制中这种经典的奇异性外，我们还表明，在该系统中清楚地看到了shubnikov-de haas效应。我们还研究了该系统中电导的统计特性。特别是……对关键电导分布进行了详细分析。在边缘状态的存在下，已经表明，电导的临界分布表现出广泛的分布，其宽度是电导量子的顺序。对于没有边缘状态的系统，与网络模型相似的关键分布已经获得了潜在障碍的模型，这表明了关键分布的宇宙。在2006年，我们研究了量子霍尔电线中潜在相关性的影响，并发现了潜在相关性引入的意外功能。在实际材料中，杂质潜力具有有限的电位范围，因此该疾病的潜力具有有限的相关长度。因此，重要的是要考虑潜在相关以及电子相关的影响。在没有杂质的情况下，量子大厅电线的电导在宽大的Landau水平上显示出量化的步骤。在存在杂质的情况下，杂质散射将边缘状态与散装状态混合在一起，并且在电导高原过渡时，电导率变小。我们发现，当电势相关长度大于磁长度时，小电导区域就会如预期的那样消失。除此之外，我们还意外地发现，电导步骤转向更高的能量。此新功能特定于长电线。我们已经半经典地认为，由于疾病的潜力平稳，转变是边缘状态反射的结果。较少的