RUI: Highly Correlated Systems of Reduced Dimensionality: A Study of the Fractional Quantum Hall Effect

[9420560]提出了数值工作来研究在横向磁场作用下二维电子气体中所观察到的分数量子化霍尔效应现象中的一些突出问题。该电子层形成于高质量镓砷异质结构半导体器件的半导体界面上。提出的研究涉及在最低朗道能级占据的偶数部分形成的费米-液体状态的性质和性质，新的对偶子量子霍尔态及其稳定的物理条件，边缘态，量子流体到经典维格纳晶体的转变，以及量子霍尔态的光学性质。本研究旨在了解镓-砷异质结构器件中制备的电子（电流的载流子）系统的行为，该系统在空间上被限制在一个平面上，并受垂直磁场的影响。在适当的条件下，电子表现出分数量子霍尔效应。这种现象是由于电子凝结成一种高度集合体的状态，与它们最初的个体特征几乎没有什么相似之处。这是量子力学的亚原子领域——一个相当有趣的科学领域。此外，量子霍尔效应在半导体工业中具有潜在的技术应用。这项RUI研究将在加州州立大学洛杉矶分校进行，这是一所以本科生为主的少数民族大学，将涉及本科生和硕士生。

9420560 Rezayi Numerical work is proposed to investigate some outstanding problems in the phonomenon of 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 semi-conductor interface of a high quality gallium-arsenic heterostructure semi-conductor device. The proposed research addresses the nature and properties of the Fermi-Liquid state formed at even fractions of the lowest Landau level occupation, novel parafermion quantum Hall states and the physical conditions which stabilize them, edge states, the quantum fluid to classical Wigner crystal transition, and optical properties of quantum Hall state. %%% This research is aimed at understanding the behavior of a system of electrons (carriers of electric current) confined spatially to a plane and subject to a perpendicular magnetic field as prepared in gallium-arsenic heterostructure devices. Under suitable conditions the electrons exhibit the phenomenon of Fractional Quantum Hall Effect. The phenomenon results from the condensation of electrons into a highly collective state with the little semblance of their initial individual characteristics. This is the subatomic realm of quantum mechanics - an area of considerable scientific interest. In addition, the quantum Hall effect has potential technological applications in semiconductor industry. This RUI research will be carried out at California State University, Los Angeles - a predominantly undergraduate minority institution - and will involve both undergraduate and Master's level students.