Theoretical Studies of the Quantum Hall Effect and NonlinearMesoscopic Transport

9301433约翰逊本理论研究将研究整数和分数量子霍尔效应（IQHE和IQHE）的基本传输和微观特性。 一种新的方法来输运的IQHE已经开发，并将适用于非线性介观输运和应用于研究非线性时间无关和时间相关的影响设备。 在IQHE这种方法将被用来研究电流分布和无耗散IQHE，目前还没有很好地理解的基本属性的崩溃。 我们将研究基于这种击穿现象发展一种新型的可调谐声子或光子激光器的可能性。 该研究将包括一个详细的研究性质和实验结果的边缘激发在复杂的分数，并调查适当的描述散装准粒子激发。 这些对于理解微生物学的微观结构是很重要的。 最后，基于密度泛函理论的方法将被开发，这将提供一个强大的数值工具来研究在强磁场中的非均匀电子气的性质。 这项研究涉及现代凝聚态物理学中最重要的当前问题之一。 研究的重点是在一定条件下，在强磁场中半导体界面处形成的一种新的物质状态的性质。 这种“二维电子气”有许多不寻常的性质。 除了基本的利益，这些性质可能有新的和新颖的电子器件的应用。 这项工作将集中在非线性传输现象和密度泛函制定的问题。 这些都是没有得到大量关注的主题。 ***

9301433 Johnson This theoretical research will study fundamental transport and microscopic properties in the integer and fractional quantum Hall effects (IQHE and FQHE). A novel approach to transport in the IQHE has been developed and will be adapted to nonlinear mesoscopic transport and applied to the study of nonlinear time-independent and time-dependent effects in devices. In the IQHE this approach will be used to study current distributions and the breakdown of dissipationless IQHE, fundamental properties which are not presently well understood. The possibility of developing a novel tunable phonon or photon laser, based on the breakdown, will be studied. The FQHE research will include a detailed study of the properties and experimental consequences of edge excitations at complicated fractions, and an investigation of the appropriate description of bulk quasiparticle excitations. These are important to understand the microscopics of the FQHE. Finally, a method based on density functional theory will be developed which will provide a powerful numerical tool to study the properties of an inhomogeneous electron gas in a strong magnetic field. %%% The research conducted on this grant deals with one of the most important current problems in modern condensed matter physics. The research focuses on the properties of a new state of matter which is formed in a strong magnetic field at a semiconductor interface under certain conditions. This "two-dimensional electron gas" has many unusual properties. Besides being of fundamental interest, these properties may have application to new and novel electronic devices. The work will concentrate on nonlinear transport phenomena and a density functional formulation of the problem. These are topics which have not received a great deal of attention. ***