Correlated Electron Transport in Mesoscopic Structures

非技术总结该奖项支持理论研究和教育，以调查一类新的绝缘材料的电子特性。量子物理学已经建立了导致两大类材料的根本原因：那些导电的，导体，和那些不导电的，绝缘体。这种区别来自于绝缘体中存在的“能隙”，带电粒子必须克服这个能隙才能产生电流。量子力学还解释了半导体的性质，半导体是制造晶体管的材料。按照严格的分类，它们是绝缘体，但具有相对较小的能隙。半导体物理学已经发展出控制差距的方法，从而控制半导体的性质，使它们能够随意导电或中断导电。基于这些原理，半导体器件推动了信息技术革命。最近量子力学的应用预言了一种新的绝缘体的存在，称为“拓扑绝缘体”。“这些材料必须在材料的主体中具有电荷载流子的能隙;然而，主体绝缘体与材料表面和边缘的导电通道共存。在足够低的温度下，边缘通道被预测为电子的理想导体。另一个值得注意的预测是，拓扑绝缘体和超导体之间界面的边缘通道必须容纳所谓的马约拉纳态。在足够低的温度下，超导材料发展出一种新的量子态，对电流没有电阻。马约拉纳态是一种新的量子力学态，可以作为量子计算机的基础，从而有望再次彻底改变数字技术。然而，在现实中，即使以半导体物理学的标准来看，任何现有拓扑绝缘体中的电子能隙都相当小。小的差距放大了材料缺陷的不利影响，并且使得难以控制拓扑绝缘体的传导和获取边缘沟道的不寻常性质。该项目的目标是确定掩盖拓扑绝缘体边缘通道理想电导的机制，通过测量拓扑绝缘体与超导体结合的系统对微波的吸收情况来检测Majorana状态，并探索增加Majorana状态鲁棒性的方法。本研究中考虑的系统有望成为未来电子技术的潜在元素。因此，这个基础科学项目可能会产生技术影响。这个项目的工作发展的理解真实的材料和凝聚态理论的现代方法的熟练程度。它为研究生和博士后研究人员提供了一个良好的培训基地。技术总结该奖项支持理论研究和教育，以调查介观系统的频率相关响应。重点放在理论适用于实验涉及的边缘状态在二维拓扑绝缘体和超导纳米电路。动机来自于新材料合成的进步，实验技术使静态和动态响应的高精度测量成为可能，以及评估这些响应对理论提出的挑战。在两个介观系统的响应函数的对称性和非微扰相互作用的影响的表现形式的搜索形成的共同主题，团结的所有部分的proposal.The项目的第一部分是致力于调查的有限温度电阻和磁阻的一维电子通道的边缘的二维拓扑绝缘体。要理解电阻和磁阻，需要发展一维螺旋电子态介导的电荷无序和自旋相关理论。该项目的第二部分旨在发展在凝聚态中寻找马约拉纳费米子的新方法。主要目标是在半导体纳米线间约瑟夫森结的低频响应函数和微波谱中发现Majorana态的特征。项目的第三部分研究了具有强对相互作用和自旋轨道耦合的一维费米系统的激发谱和动力学响应。目标是发展适用于各种新型凝聚态系统的理论方法。该项目的所有部分都是由实验介观物理学激发的。解决该项目中提出的问题可以解释现有的实验结果，有助于计划新的实验，并导致开发广泛适用于低维量子凝聚态的理论方法。

NON-TECHNICAL SUMMARYThis award supports theoretical research and education to investigate the electronic properties of a new class of insulating materials. Quantum physics has established the underlying reason that leads to two broad classes of materials: those which conduct electricity, conductors, and those that do not, insulators. The distinction comes from the existence in the insulators of an "energy gap" that charged particles have to overcome in order to produce an electric current. Quantum mechanics also explains the properties of semiconductors, the materials from which transistors are made. By strict classification these are insulators, but with a relatively small energy gap. Semiconductor physics has developed ways to control the gap, and thus to control the properties of semiconductors, making them able to conduct electricity or interrupt the conduction at will. Built on these principles semiconductor devices have fueled the information technology revolution. Recently application of quantum mechanics has predicted the existence of a new kind of insulator called "topological insulators." These materials must have an energy gap for charge carriers in the bulk of the material; however, the bulk insulator coexists with conducting channels at the surfaces and edges of the material. At sufficiently low temperatures the edge channels are predicted to be ideal conductors for electrons. Yet another remarkable prediction is that the edge channels at the interface between a topological insulator and a superconductor must house so-called Majorana states. At sufficiently low temperature, superconducting materials develop a new quantum state that has no resistance to electric current. Majorana states are qualitatively new quantum mechanical states which may be used as the foundation for a quantum computer; thus carrying a promise to revolutionize the digital technology once again. However, in reality the electron energy gap in the bulk of any existing topological insulator is quite small, even by the standards of semiconductor physics. The smallness of the gap amplifies the adverse effects of materials imperfections and makes it difficult to control the conduction of topological insulators and to harvest the unusual properties of the edge channels. The goal of this project is to determine the mechanisms that obscure the ideal conductance of edge channels in topological insulators, find ways to detect Majorana states by measuring how well microwaves are absorbed by systems of topological insulators combined with superconductors, and to explore ways of increasing the robustness of Majorana states.The systems considered in this research hold promise to be potential elements of a future electronics technology. Therefore this fundamental science project may have a technological impact. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory. It provides a good training ground for graduate students and post-doctoral research associates.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate the frequency dependent responses of mesoscopic systems. The emphasis is placed on theory applicable to experiments involving the edge states in two-dimensional topological insulators and with superconducting nanocircuits. The motivation comes from the advances in synthesis of new materials, experimental techniques enabling the high-precision measurements of static and dynamic responses, and from the challenges of evaluation of these responses present for the theory. The search for manifestations of symmetries and non-perturbative interaction effects in the response functions of the two mesoscopic systems forms the common theme that unites all parts of the proposal.The first part of the project is devoted to investigation of the finite-temperature resistance and magnetoresistance of one-dimensional electron channels at the edges of a two-dimensional topological insulator. Understanding the resistance and magnetoresistance calls for the development of a theory of charge disorder and spin correlations mediated by the one-dimensional helical electron states.The second part of the project is aimed to develop new methods in the search for Majorana fermions in condensed matter. The main goal is to find the signatures of Majorana states in low-frequency response functions and in microwave spectra of Josephson junctions between semiconductor nanowires.The third part of the project addresses the excitation spectra and dynamic responses of one-dimensional Fermi systems with strong pairing interactions and spin-orbit coupling. The goal is to develop theory methods applicable to a variety of novel condensed matter systems.All parts of the project are motivated by experimental mesoscopic physics. Solving the problems formulated in the project may explain the existing experimental results, help in planning new experiments, and lead to developing theoretical methods broadly applicable to low-dimensional quantum condensed matter.