Properties of Correlated and Multilayer Two-Dimensional Systems

将对二维量子半导体系统进行理论研究，研究在有和没有磁场的情况下无序、有限温度和独特器件结构的影响。本文将考虑维格纳晶体中边缘在强磁场中的行为，并研究边缘电子在各种情况下的弛豫、重建和熔化的计算方法。将考虑这种效应的输运和电磁吸收的后果。将使用变分波函数方法对Wigner晶体中的缺陷进行详细研究，这将有助于确定量子涨落的重要性，并将是理解熔化转变和有限温度输运的第一步。将研究量子霍尔体系中的边缘态，重点是无序对这类系统的低洼激发的影响。最后，将仔细研究两层体系中潜在不均匀性对面间隧道的影响。这项理论研究将集中于一种新的物质状态的性质，这种状态与一种在二维空间内强相互作用的电子气体有关。通常这种物质状态是在强磁场中的半导体界面处发现的。这种电子气体的一种可能结果是凝结成晶体状态，即维格纳晶体。本研究将研究这种维格纳晶体的行为。除了具有基本的物理意义外，这项研究还可能对微电子学产生影响。

Theoretical investigations will be carried out on two-dimensional quantum semiconductor systems studying effects of disorder, finite temperatures and unique device structures with and without a magnetic field. The behavior of edges in the Wigner crystal regime in a strong magnetic field will be considered and a method for calculating relaxation, reconstruction and melting of the edge electrons under various circumstances will be studied. The consequences of transport and electromagnetic absorption of such effects will be considered. A detailed study of defects in the Wigner crystal will be undertaken using a variational wavefunction approach which should help determine the importance of quantum fluctuations and will be a first step in understanding both the melting transition and finite temperature transport. Edge states in the quantum Hall regime will be studied with emphasis on the effects disorder may have on the low-lying excitations of such systems. Finally, a careful study of the influence of potential inhomogeneities in a two-layer system on interplane tunneling will be undertaken. %%% This theoretical study will focus on the properties of a new state of matter associated with a gas of strongly interacting electrons confined to two-dimensions. Usually this state of matter is found at the semiconductor interface in a strong magnetic field. One possible outcome of this electron gas is to condense into a crystalline state, the Wigner crystal. The research will study the behavior of this Wigner crystal. Besides being of fundamental physical interest, there may be ramifications of this research on microelectronics.