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

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，我们研究了二维系统在具有固定符号的无序磁场中的输运性质。该模型对应于磁场的随机涨落与其平均值具有相同量级的情况。二维随机磁场系统起源于分数量子霍尔系统理论，其中电子关联起着重要作用。然后，它已被发现的系统没有边缘状态的电导是不敏感的磁场的波动的强度和停留在弱磁场的限制电导量子的顺序。这种奇异的行为可以在德鲁德公式的框架内理解。除了弱场极限下的经典奇异性外，我们还证明了在该系统中存在明显的Shubnikov-de哈斯效应，并研究了该系统电导的统计性质。特别是， ...更多信息 详细分析了临界电导的分布。在边缘态的存在下，它已被证明，电导的临界分布表现出宽的分布，其宽度是电导量子的顺序。对于没有边缘态的系统，我们得到了类似于网络模型和势无序模型的临界分布，表明了临界分布的普遍性。2006年，我们研究了量子霍尔线中的势关联效应，发现了势关联引入的一些意想不到的特性。在真实的材料中，杂质势具有有限的势范围，因此无序势具有有限的关联长度。因此，重要的是要考虑电位相关以及电子相关的影响。在没有杂质的情况下，量子霍尔线的电导在体朗道能级上呈现量子化阶跃。在杂质的存在下，杂质散射混合的边缘状态与体状态和电导变得指数小的电导平台过渡。我们发现，当势关联长度大于磁长度时，小电导区如预期的那样消失。除此之外，我们还意外地发现电导阶跃向高能方向移动。这一新功能是专门针对长导线的。我们认为，半经典的转变是由于平滑变化的无序势的边缘状态的反射的后果。少

项目成果

Shubnikov-de Haas effect on conductance fluctuations in two-dimensional random magnetic fields

二维随机磁场中电导涨落的舒布尼科夫-德哈斯效应

• 发表时间: 2006
• 期刊: Physica E 34
• 作者: Y. Nagai;H. Akera and H. Suzuura;T.Kawarabayashi
• 通讯作者: T.Kawarabayashi

Electron diffusion in a two-dimensional disordered symplectic system with electron-phonon interactions

具有电子-声子相互作用的二维无序辛系统中的电子扩散

• 发表时间: 2005
• 期刊: Journal of the Physical Society of Japan 74
• 作者: S.Kanamaru;H.Suzuura;H.Akera;H.Watanabe
• 通讯作者: H.Watanabe

Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign

具有固定符号的无序磁场中二维系统的量子输运特性

• 发表时间: 2005
• 期刊: Physical Review B 71
• 作者: S.Kanamaru;H.Suzuura;H.Akera;H.Watanabe;T. Ise;T.Kawarabayashi
• 通讯作者: T.Kawarabayashi

Quantum transport pro perties of two-dimensional systems in disorder ed magnetic fields with a fixed sign

固定符号无序磁场中二维系统的量子输运特性

• 发表时间: 2005
• 期刊: Physical Review B 71
• 作者: S.Kanamaru;H.Suzuura;H.Akera;H.Watanabe;T. Ise;T.Kawarabayashi;H. Akera;H.Watanabe et al.;T.Kawarabayashi et al.
• 通讯作者: T.Kawarabayashi et al.