Theoretical Studies of the Quantum Hall Effect and Nonlinear Mesoscopic Transport

该奖项支持理论研究，以研究整数和分数量子霍尔效应的基本性质，并研究介观输运。PI发展了系综密度泛函理论方法来研究量子点等大型非均匀系统中的分数量子霍尔效应。该理论允许包含电子关联、自旋、任意限制、有限层厚度、朗道能级混合和有限温度。系综密度泛函理论将被用于研究量子点在大磁场中的性质。与加成光谱、磁致发光和隧穿实验相比，将显示测量的特征是如何由电子密度、关联态、自旋和边缘结构的变化而产生的。系综密度泛函理论将进一步发展到包含分数量子霍尔效应的非对角长程有序，并将其应用于量子点。PI还计划研究量子霍尔系统的边缘模式。这项研究的重点是最近的实验数据，对于这些数据，勒廷格液体描述在不应该适用的情况下适用。PI打算测试这是否是最低朗道水平相关性的结果。系综密度泛函理论将被用来研究不同条件下点的边缘结构。PI研究的另一个主旨涉及他为稳态介观系统发展的输运公式，该公式在线性响应区域之外有效。形式主义将被应用于研究特定的非理想系统，包括量子点接触。PI计划探索模型系统，将他的方法与非平衡格林函数等传统方法进行比较，目的是深入了解稳态高度非平衡统计力学，包括边界条件的作用。该奖项支持强磁场中量子点的理论研究和介观器件的输运特性。这项研究将使用最先进的方法，包括材料的特定性质和特定的几何形状，以研究可能出现在强磁场中的新电子态。这项研究是基础性的，但也为发展21世纪的电子设备技术奠定了基础。拟议的工作为培养下一代凝聚态理论家提供了教育机会。*

This award supports theoretical research to study fundamental properties of the integer and fractional quantum Hall effects, and to study mesoscopic transport. The PI has developed an ensemble density functional theory approach to study the fractional quantum Hall effect in large inhomogeneous systems such as quantum dots. The theory enables the inclusion of electron correlations, spin, arbitrary confinements, finite layer thickness, Landau-level mixing and finite temperature. The ensemble density functional theory will be used to study the properties of quantum dots in large magnetic fields. Comparison with addition spectrum, magnetoluminescence, and tunneling experiments will show how measured features result from changes in electron density, correlation state, and spin and edge structures. The ensemble density functional theory will be further developed to include the off-diagonal long-range order of the fractional quantum Hall effect and then applied to quantum dots. The PI also plans to study the edge modes of quantum Hall systems. The focus of this research is on recent experimental data for which a Luttinger liquid description works when it should not. The PI intends to test whether this is a consequence of correlations in the lowest Landau level. The ensemble density functional theory will be used to investigate edge structures under different conditions in dots.Another thrust of the PI's research involves a transport formalism that he developed for steady-state mesoscopic systems which is valid beyond the linear response regime. The formalism will be applied to study specific non-ideal systems, including quantum point contacts. The PI plans to explore model systems comparing his approach to traditional approaches, such as nonequilibrium Green's functions, with the aim of gaining insight into steady-state highly nonequilibrium statistical mechanics including the role of boundary conditions. %%%This award supports theoretical research on quantum dots in high magnetic fields and in transport properties of mesoscopic devices. The research will use state-of-the-art methods that can include materials specific properties and specific geometries to study possible new electronic states that are believed to occur in high magnetic fields. This research is fundamental, but lays groundwork that may be important for developing the electronic device technologies of the 21st century. The proposed work provides educational opportunities for training the next generation of condensed matter theorists.***