RUI: Collective Phenomena in Highly Correlated Systems: Study of the Fractional Quantum Hall Effect

本科院校研究的更新奖是 继续研究分数量子霍尔效应 数值工作提出了调查突出的问题， 分数量子化霍尔效应，这是观察到的两个- 三维电子气受到横向磁场的影响。 电子层形成在半导体的半导体界面处， 高质量砷化镓异质结构器件。 近期 非常高的流动性样品的可用性提供了独特的 探索极端强相关系统的机会 量子力学极限，集体现象发生的地方。 在 此外，量子霍尔的最新光学测量结果 国家提供了另一个维度的实验性探索， 量子霍尔效应 拟议的研究涉及 半积分性质与分数阶态 量子霍尔效应以及 稳定他们。 其他研究领域包括了解 边缘态;量子流体与经典维格纳晶体交叉， 量子霍尔态的光学特征; 分数量子霍尔效应的可能性 电子空穴流体 还提出了一个有限大小的数值 Kalmeyer-Laughlin手征哈密顿量模型的研究 自旋流体基态是精确的。 手性自旋流体与 量子霍尔状态和支持分数统计（半元） 兴奋。 %%% 量子霍尔效应是由于物质的一种独特状态-- 三维电子流体 电子的合作行为 在二维空间中的行为与在 更熟悉的三维空间。 该研究将使用 数值和分析技术来研究一些属性 这个奇怪的二维系统， 兴趣 除了提供深入了解的基础物理， 这种奇怪的物质状态，其结果也可能是有趣的 用于器件制造和高温超导性。

This renewal award for Research at Undergraduate Institutions is for continued research on the fractional quantum Hall effect. Numerical work is proposed to investigate outstanding problems in the fractionally quantized Hall effect which is observed in a two- dimensional electron gas subject to a transverse magnetic field. The electron layer is formed at the semiconductor interface of a high quality Gallium-Arsenide heterostructure device. The recent availability of very high mobility samples offers a unique opportunity to probe strongly correlated systems in the extreme quantum mechanical limit, where collective phenomena occur. In addition, the more recent optical measurements of the quantum Hall states have provided another dimension in experimental probes of the quantum Hall effect. The proposed research addresses the nature of half-integral and hierarchy states of the fractional quantum Hall effect as well as the physical conditions which stabilize them. Additional areas of research include understanding edge states; the quantum fluid to classical Wigner crystal cross- over; optical signature of quantum Hall states; and, the possibility of fractional quantum Hall effect in a two-dimensional electron-hole fluid. Also proposed is a finite-size numerical study of a model Hamiltonian for which the Kalmeyer-Laughlin chiral spin fluid ground state is exact. Chiral spin fluids are similar to quantum Hall states and support fractional statistics (semion) excitations. %%% The quantum Hall effect is due to a unique state of matter - a two- dimensional electron fluid. The cooperative behavior of electrons in two-dimensions is markedly different from their behavior in the more familiar three-dimensions. The proposed research will use numerical and analytical techniques to study a number of properties of this strange two-dimensional system which are of current interest. Besides providing insight into the underlying physics of this strange state of matter, the results may also be of interest in device fabrication and for high temperature superconductivity.