Correlated Electron Transport in Mesoscopic Structures

介观结构中的相关电子传输

• 批准号: 1206612
• 负责人: Leonid Glazman
• 金额: $ 54万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206612&HistoricalAwards=false
• 关键词: Correlated; Electron; Transport; Mesoscopic; Structures

TECHNICAL SUMMARYThis award supports theoretical investigation of the static and time-varying responses of mesoscopic systems. The emphasis is placed on theory applicable to experiments on topological insulators and superconducting nano-circuits. The motivation comes from the recent advances in nanofabrication, synthesis of new materials, and precise experimental techniques of microwave and time-resolved measurements, as well as from the theoretical challenges inherent in the evaluation of the response functions. The common thread of the entire project is the importance of electron interactions and symmetries in the responses of the mesoscopic systems.The project is composed of three parts on:(1) Investigation of the finite-temperature conductance of one-dimensional electron channels at the edges of a two-dimensional topological insulator. Here, the conductance evaluation calls for the development of a theory for inelastic electron backscattering in one-dimensional helical electron liquids. The PI and his group aim at deriving a low-energy theory valid for a generic interacting helical edge state which respects time-reversal invariance, but may not conserve any of the electron spin projections(2) Analysis of the conduction of thin films of three-dimensional topological insulators. The intrinsic disorder in these materials results in their substantial bulk conductivity, which shunts the electron transport within the topologically-protected conducting state at the surface. The aim is to build a comprehensive theory for such experiments. (3) Addressing the scattering of microwave photons off a weak link in an array of Josephson junctions. This bosonic version of the quantum impurity problem has a number of common traits with its electronic counterpart, but allows one an experimental access to a different set of response functions. Like in the first part of the project, the aim is to develop a theory for inelastic scattering. The award will also support the PI's educational activities integrated with the above research at the undergraduate, graduate, and postdoctoral levels. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory. The PI will also organize optical workshops geared towards broad representation of scientists from diverse backgrounds. NON-TECHNICAL SUMMARYHow matter responds when an electric current passes through it or when electromagnetic waves interact with it depends on the size of the sample. Upon decreasing size new properties that are not observed in bulk materials may emerge. Quantum interference and interaction of electrons or quanta of light, called photons, result in properties emerging on the meso-scale - a scale small enough to preserve coherence, but large compared to the atomic scales. This project aims at theoretical investigation of a number of new experimentally accessible systems which are expected to display unusual mesoscopic behavior. The systems of interest include two and three-dimensional topological insulators, which do not conduct electricity through the bulk but are perfect conductors for currents passing through their edges or boundaries, photons interacting with scattering centers in small-scale superconducting circuits. All such systems are currently viewed as potential elements of future electronic technology. The theoretical research to be carried out on this project will help in achieving an understanding of real materials exhibiting various exotic properties at the mesoscale and could potentially lead to the design of new technologically important devices.The award will also support the PI's educational activities integrated with the above research at the undergraduate, graduate, and postdoctoral levels. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory. The PI will also organize optical workshops geared towards broad representation of scientists from diverse backgrounds.

该奖项支持对介观系统的静态和时变响应的理论研究。重点放在拓扑绝缘体和超导纳米电路实验的理论应用上。其动机来自纳米制造、新材料合成、微波和时间分辨测量的精确实验技术的最新进展，以及响应函数评估中固有的理论挑战。整个项目的共同主线是电子相互作用和对称性在介观系统响应中的重要性。本课题由三个部分组成：(1)二维拓扑绝缘体边缘一维电子通道的有限温度电导研究。在这里，电导评估需要发展一维螺旋电子液体中的非弹性电子后向散射理论。PI和他的团队的目标是推导出一种低能理论，适用于一般相互作用的螺旋边缘状态，该状态尊重时间反转不变性，但可能不保留任何电子自旋投影(2)三维拓扑绝缘体薄膜的导电分析。这些材料的内在无序性导致它们具有大量的体积导电性，从而在表面的拓扑保护导电状态下分流电子传输。其目的是为这类实验建立一个全面的理论。(3)解决微波光子在约瑟夫森结阵列中弱链路的散射问题。这种玻色子版本的量子杂质问题与电子版本有许多共同的特征，但允许一个实验访问不同的响应函数集。和项目的第一部分一样，目标是发展一种非弹性散射理论。该奖项还将支持PI在本科，研究生和博士后阶段的教育活动与上述研究相结合。研究结果将被纳入PI的量子多体物理和凝聚态理论研究生课程。PI还将组织光学研讨会，面向来自不同背景的科学家的广泛代表。当电流通过或电磁波与物质相互作用时，物质的反应取决于样品的大小。随着尺寸的减小，可能会出现在散装材料中没有观察到的新特性。量子干涉和电子或光量子（称为光子）的相互作用导致了中观尺度上出现的特性——中观尺度小到足以保持相干性，但与原子尺度相比却很大。本项目旨在理论研究一些新的实验可获得的系统，这些系统有望显示不寻常的介观行为。感兴趣的系统包括二维和三维拓扑绝缘体，它们不导电，但对于电流通过其边缘或边界是完美的导体，光子与小规模超导电路中的散射中心相互作用。所有这些系统目前都被视为未来电子技术的潜在组成部分。在这个项目上进行的理论研究将有助于理解在中尺度上表现出各种奇异特性的真实材料，并可能导致设计新的技术上重要的设备。该奖项还将支持PI在本科，研究生和博士后阶段的教育活动与上述研究相结合。研究结果将被纳入PI的量子多体物理和凝聚态理论研究生课程。PI还将组织光学研讨会，面向来自不同背景的科学家的广泛代表。