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

本科生研究续展奖是为了表彰对分数量子霍尔效应的持续研究。用数值方法研究了在横向磁场作用下的二维电子气中观察到的分数量子化霍尔效应中的突出问题。电子层形成在高质量的镓-砷异质结器件的半导体界面上。最近出现的非常高迁移率的样品为在极端量子力学极限下探测强关联系统提供了一个独特的机会，在极端量子力学极限下，集体现象会发生。此外，最近对量子霍尔态的光学测量为量子霍尔效应的实验探测提供了另一个维度。这项研究解决了分数量子霍尔效应的半积分态和层次态的性质，以及稳定它们的物理条件。其他研究领域包括理解边缘状态；量子流体到经典Wigner晶体的交叉；量子霍尔态的光学特征；以及二维电子-空穴流体中分数量子霍尔效应的可能性。对Kalmeyer-Laughlin手征自旋流体基态是精确的模型哈密顿量进行了有限尺寸的数值研究。手性自旋流体类似于量子霍尔态，支持分数统计(Semion)激发。量子霍尔效应是由于物质的一种独特状态--二维电子流体。电子在二维空间中的合作行为与它们在更常见的三维空间中的行为明显不同。这项拟议的研究将使用数值和分析技术来研究这个奇怪的二维系统的一些当前感兴趣的性质。除了提供了对这种奇怪物质状态的基本物理的洞察，这些结果也可能对器件制造和高温超导感兴趣。

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.