Correlated Electron Transport in Mesoscopic Structures

非技术总结该奖项支持理论研究和教育，以研究一种新型绝缘材料的电子性能。量子物理学已经确定了导致两大类材料的根本原因：导电的材料是导体，而不导电的材料是绝缘体。这种区别来自于绝缘体中存在一个“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，这些是绝缘体，但具有相对较小的能隙。半导体物理学已经开发出控制缝隙的方法，从而控制半导体的性质，使它们能够随意导电或中断导电。在这些原则的基础上，半导体设备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，这种绝缘体被称为“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，主体绝缘体在材料的表面和边缘与导电沟道共存。在足够低的温度下，边缘沟道被预测为电子的理想导体。另一个值得注意的预测是，在拓扑绝缘体和超导体之间的交界处的边缘通道必须包含所谓的Majorana态。在足够低的温度下，超导材料会形成一种新的量子态，对电流没有阻力。Majorana态本质上是一种新的量子力学状态，可以用作量子计算机的基础；因此，它承诺再次给数字技术带来革命性的变化。然而，事实上，即使按照半导体物理的标准，现有的任何拓扑绝缘体中的大部分电子能隙也是相当小的。微小的间隙放大了材料缺陷的不利影响，使控制拓扑绝缘子的导通和获取边缘沟道的异常特性变得困难。该项目的目标是确定在拓扑绝缘体中掩盖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程度来找到检测Majorana状态的方法，并探索增加Majorana状态的稳健性的方法。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，这项基础科学计划可能会产生技术影响。这个项目的工作增进了对真实材料的理解，并熟练掌握了现代凝聚态理论的方法。它为研究生和博士后研究协会提供了一个很好的培训基础。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。重点介绍了适用于二维拓扑绝缘体边缘态实验和超导纳米电路实验的理论。其动机来自于新材料合成方面的进步，以及能够高精度测量静态和动态响应的实验技术，以及对这些响应的评估对理论提出的挑战。在这两个介观系统的响应函数中寻找对称性和非微扰相互作用效应的表现形式形成了统一的共同主题。项目的第一部分致力于研究二维拓扑绝缘体边缘的一维电子通道的有限温度电阻和磁阻。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关联理论。该项目的第二部分旨在开发在凝聚态中寻找Majorana费米子的新方法。主要目的是在半导体纳米线之间约瑟夫森结的低频响应函数和微波光谱中找到Majorana态的特征。项目的第三部分研究了具有强配对相互作用和自旋-轨道耦合的一维费米系统的激发光谱和动态响应。该项目的目标是开发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推动的。解决项目中提出的问题可能会解释现有的实验结果，有助于规划新的实验，并导致开发出广泛适用于低维量子凝聚物质的理论方法。

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.