Correlated Electron Transport in Mesoscopic Structures

技术总结该奖项支持介观系统静态和时变响应的理论研究。重点介绍了适用于拓扑绝缘体和超导纳米电路实验的理论。其动机来自纳米制造、新材料的合成、微波和时间分辨测量的精确实验技术方面的最新进展，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体系响应中的重要性。该项目由三个部分组成：(1)研究二维拓扑绝缘体边缘一维电子通道的有限温度电导。在这里，电导的评估要求发展一维螺旋电子液体中的非弹性电子背散射理论。Pi和他的团队旨在推导一个适用于一般相互作用的螺旋边态的低能理论，该理论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导电分析。这些材料的本征无序导致其大量的体导电性，这分流了表面拓扑保护的导电态内的电子传输。其目的是为这类实验建立一个全面的理论。(3)解决约瑟夫森结阵列中弱链上微波光子的散射问题。这种玻色子版本的量子杂质问题与电子杂质问题有许多共同的特征，但允许人们通过实验获得一组不同的响应函数。像该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在本科生、研究生和博士后层面与上述研究相结合的教育活动。这项研究的成果将被纳入PI关于量子多体物理和凝聚态理论的研究生水平课程。国际和平研究所还将组织光学讲习班，面向来自不同背景的科学家的广泛代表。非技术总结电流通过物质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。当尺寸减小时，可能会出现在大块材料中没有观察到的新特性。量子干涉和电子或光量子的相互作用，称为光子，导致在介观尺度上出现性质--这个尺度足够小，可以保持相干性，但与原子尺度相比，它很大。这个项目旨在对一些新的实验可达系统进行理论研究，这些系统有望显示出不寻常的介观行为。感兴趣的系统包括两个和三维拓扑绝缘体，它们不通过块体导电，但对于通过其边缘或边界的电流来说是完美的导体，光子与小型超导电路中的散射中心相互作用。目前，所有这些系统都被视为未来电子技术的潜在组成部分。对这个项目进行的理论研究将有助于理解真实材料在中尺度上表现出的各种奇异性质，并可能导致新的重要技术设备的设计。该奖项还将支持PI在本科生、研究生和博士后层面与上述研究相结合的教育活动。这项研究的成果将被纳入PI关于量子多体物理和凝聚态理论的研究生水平课程。国际和平研究所还将组织光学讲习班，面向来自不同背景的科学家的广泛代表。

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.