Theoretical Studies of the Quantum Hall Effect and Nonlinear Mesoscopic Transport

该奖项支持研究整数和分数量子霍尔效应的基本性质，以及研究介观输运的理论研究。PI开发了一种集成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相关、自旋、任意约束、有限层厚度、朗道能级混合和有限温度。将利用系综密度泛函理论研究大磁场下量子点的性质。通过与附加光谱、磁致发光和隧道实验的比较，可以看出电子密度、相关态、自旋和边缘结构的变化是如何产生测量特征的。将进一步发展包含分数量子霍尔效应的非对角长程阶的系综密度泛函理论，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，其中Luttinger液体描述在不应该的情况下起作用。该指数打算检验这是否是最低朗道水平相关性的结果。利用系综密度泛函理论研究不同条件下点的边缘结构。PI研究的另一个重点涉及他为稳态介观系统开发的输运形式，该输运形式在线性响应体系之外有效。该形式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，将他的方法与传统方法（如非平衡格林函数）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。该奖项支持高磁场下量子点和介观器件输运特性的理论研究。这项研究将使用最先进的方法，包括材料的特定特性和特定的几何形状，来研究在高磁场中可能出现的新电子状态。这项研究是基础性的，但为21世纪电子设备技术的发展奠定了重要的基础。提出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.***