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

9420560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现象中的一些突出问题。电子层形成在高质量镓砷异质结半导体器件的半导体界面上。这项研究涉及在最低Landau能级占有率的偶数分数处形成的费米液态态的性质和性质、新的准费米量子霍尔态及其稳定的物理条件、边缘态、量子流体到经典Wigner晶体的跃迁以及量子霍尔态的光学性质。这项研究旨在了解在镓-砷异质结器件中制备的电子系统(电流的载流子)在空间上被限制在平面上并受到垂直磁场的行为。在合适的条件下，电子表现出分数量子霍尔效应现象。这种现象是由于电子凝聚成高度集体的状态，与它们最初的个体特征几乎没有什么相似之处。这就是量子力学的亚原子领域--这是一个极具科学价值的领域。此外，量子霍尔效应在半导体工业中具有潜在的技术应用前景。这项研究将在加州州立大学洛杉矶分校进行，将涉及本科生和硕士研究生。加州州立大学洛杉矶分校是一所以本科学生为主的少数民族院校。

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.