Anderson transitions in disordered systems and electron correlations

在2004年和2005年，我们研究了二维系统在固定符号无序磁场中的输运性质。该模型对应于磁场随机波动与其均值同阶的情况。二维随机磁场系统是在分数阶量子霍尔系统理论中出现的，其中电子相关起着重要的作用。然后发现对于没有边缘状态的系统，电导对磁场波动的强度不敏感，并且在弱磁场的极限下保持在电导量子的数量级上。这种奇异的行为可以在德鲁德公式的框架内理解。除了弱场极限中的经典奇点外，我们还证明了在这个系统中可以清楚地看到舒布尼科夫-德哈斯效应。我们还研究了这种系统中电导的统计性质。并对临界电导分布进行了详细的分析。在边缘态存在的情况下，电导的临界分布呈宽分布，其宽度是电导量子的数量级。对于无边缘状态的系统，得到了与网络模型和有位势无序模型相似的临界分布，表明了临界分布的通用性。2006年，我们研究了量子霍尔线中势相关的影响，发现了势相关引入的意想不到的特性。在实际材料中，杂质势具有有限的势范围，因此无序势具有有限的相关长度。因此，除了考虑电子相关外，还要考虑势相关的影响。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的阶跃。当杂质存在时，杂质散射使边缘态与体态混合，电导在电导平台跃迁处呈指数级小。我们发现，当电位相关长度大于磁长时，小电导区如预期的那样消失。除此之外，我们还意外地发现，电导阶向更高的能量转移。这个新功能是针对长导线的。我们已经半经典地论证了这种位移是由于平滑变化的无序势而引起的边缘状态反射的结果。少

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