Ilani S, Martin J, Teitelbaum E, Smet J H, Mahalu D, Umansky V, Yacoby A
Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
Nature. 2004 Jan 22;427(6972):328-32. doi: 10.1038/nature02230.
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.
量子霍尔效应源于当被限制在二维空间的电子受到垂直磁场作用时形成的局域态和扩展态之间的相互作用。由于粒子的局域化，该效应涉及所有电子输运性质的精确量子化。在量子霍尔效应的传统理论中，强场局域化与电子沿着无序势恒定的轮廓的单粒子漂移运动相关。探测量子霍尔相之间过渡区域中扩展态的输运实验已被用于检验该理论及其对量子霍尔相变的影响。尽管对高度无序样品的一些实验证实了单粒子图像的有效性，但其他实验和一些近期理论发现了与预测的普遍行为的偏差。在这里，我们使用扫描单电子晶体管来探测各个局域态，我们发现这些局域态与单粒子理论的预测有显著不同。这些态主要由库仑相互作用决定，并且仅在动能的量子化限制电子的屏蔽能力时才出现。我们得出结论，量子霍尔效应的区域和相变比单粒子框架所预测的具有更大的多样性。我们的实验提出了一种统一的局域化图像，其中单粒子模型仅在强无序极限下有效。
