CAREER: Non-Equilibrium Transport and Disorder Effects in Quantum Wires and Related Systems

这一职业奖将低维导体的研究与大学生和高中生的教育活动结合在一起。由于未来的纳米器件将在依赖时间的场和其他远离平衡的条件下运行，因此对纳米尺度上的非平衡输运的理解至关重要。因此，对量子线的现实描述提出了存在电子相互作用时的非平衡效应的难题。固体总是含有杂质，因此，如果不了解无序和相互作用的相互作用，就不可能理解介观输运。本研究将采用系统的分析和数值方法相结合的方法来研究量子线中远离平衡输运中的相互作用效应，以及低维介观导体中相互作用和无序的相互作用。本文主要研究了以下几个问题：1.非平衡输运。在棘轮效应中，直流电流是由空间不对称系统中的外部交流电场产生的。这种效应有望有助于未来纳米二极管、纳米开关和纳米晶体管的发展。现有关于棘轮效应的理论研究主要集中在费米-液体体系和非相互作用电子的简化模型上。然而，电子相互作用是显著的，并导致在量子线中形成Luttinger液体。所提出的研究将包括使用Keldysh技术、玻色化、重整化群、大N平均场方法和数值方法系统地研究Luttinger液体中的棘轮效应。自旋输运远离平衡。人们对介观系统中自旋输运的物理学越来越感兴趣。这一发展的一个重要部分是对产生自旋流的可能方法的研究。拟议的研究将包括对Luttinger液体中的自旋棘轮效应的理论研究。量子霍尔系统中的输运。最近关于分数带电准粒子的干涉和隧穿的实验提出了关于准粒子输运的新的基本问题，这些问题不能用标准方法来回答。这项拟议的研究将把2D电子气视为相互作用的量子线系统，并结合玻色化过程和具有猝灭无序的软物质系统理论中发展的方法。这一方法有助于解决高原过渡的问题。教育活动将包括开发一门主要针对新生的纳米科学入门课程；将与补助金相关领域的最新发展纳入常规物理课程；学生和博士后参与研究和相关活动，如期刊俱乐部；以及前往普罗维登斯市中心的高中。将在新生课程的基础上准备一份基于互联网的高中水平的教程。在智力方面，拟议的研究将促进关于强关联电子系统的知识。量子力学的基本定律早已为人所知，但多体系统的涌现性质仍然构成了一个充满困惑和惊喜的领域。这一领域的进展至关重要。所提出的研究将有益于远非平衡量子多体系统的涌现领域。这项拟议的工作将使用低维电子系统和软凝聚物质之间的类比，从而弥合硬物质物理和软物质物理之间的现有差距。拟议的研究还将产生更广泛的影响。从理论上理解量子线中的输运对于纳米电路来说至关重要。因此，这项提议的结果对多学科纳米科学界将是重要的。教育部分将促进纳米科学的发现和理解，同时促进不同水平的教学、培训和学习，并扩大代表不足的群体的参与。非技术摘要：研究重点是在纳米尺度上发现的受限几何材料的基本性质。在这些尺度下，我们通常使用的理论必须进行修改，以解释限制，这就把无序和电子之间的相互作用等问题带到了前沿。这项研究将研究这些基本问题，这些问题可能构成未来纳米设备(纳米电子学)的基础。首席研究员将为大学新生开发和教授一门纳米科学入门课程。他还将参与通过互联网和亲自接触高中生的活动。研究成果将被整合到课程材料中。

This CAREER award combines research on low-dimensional conductors witheducational activities for university and high-school students.Since future nano-devices will operate in the presence of time-dependent fields and inother far-from-equilibrium conditions, an understanding of non-equilibrium transport onthe nanoscale is crucially important. Thus, a realistic description of quantum wires raisesthe difficult problem of non-equilibrium effects in the presence of electron interactions.Solids always contain impurities, and hence an understanding of mesoscopic transport isimpossible without an understanding of the interplay of disorder and interaction. Theresearch will employ a combination of systematic analytical and numerical methods to investigate interaction effects in far-from-equilibrium transport in quantumwires and the interplay of interaction and disorder in low-dimensional mesoscopicconductors. The research will focus on the following problems:1. Non-equilibrium transport in Luttinger liquids. In the ratchet effect, a dc current isgenerated by an external ac field in a spatially asymmetric system. This effect is expectedto help in the development of future nano-diodes, nano-switches, and nano-transistors. Theexisting theoretical studies of the ratchet effect have focused on Fermi-liquid systems andsimplified models of non-interacting electrons. However, the electronic interaction issignificant and results in the formation of a Luttinger liquid in quantum wires. Theproposed research will include a systematic investigation of the ratchet effect in Luttingerliquids using the Keldysh technique, bosonisation, renormalization group, large-N mean-fieldapproach, and numerical methods.2. Spin transport far from equilibrium. There is growing interest in the physics of spintransport in mesoscopic systems. An important part of this development is the investigationof possible ways to produce a spin current. The proposed research will include a theoreticalstudy of the spin ratchet effect in Luttinger liquids.3. Transport in quantum Hall systems. Recent experiments on interference and tunnelingof fractionally charged quasi-particles raise new fundamental questions concerning quasiparticletransport which cannot be answered by standard methods. The proposed researchwill combine an approach which treats a 2D electron gas as a system of interactingquantum wires with the bosonization procedure and with the methods developed in thetheory of soft matter systems with quenched disorder. The approach can help to solve theproblem of QHE plateau transition.Educational activities will include the development of an introductorycourse in nanoscience targeted primarily at freshmen; integration of recent developments inthe fields related to the grant into the regular physics curriculum; participation ofstudents and postdocs in research and related activities such as a journal club; and outreachto Providence inner-city high schools. An internet-based high-school-level tutorial will beprepared on the basis of the freshmen course.On intellectual grounds, the proposed research will advance the knowledge aboutstrongly correlated electronic systems. The basic laws of quantum mechanics have beenknown for a long time, but emergent properties of many-body systems still constitute afield full of puzzles and surprises. Progress in this field is of fundamental importance. Theproposed research will benefit the emergent field of far-from-equilibrium quantum many-bodysystems. The proposed work will employ analogies between low-dimensional electronsystems and soft condensed matter and thus bridge the existing gap between hard and softmatter physics. The proposed research will also have broader impacts. A theoreticalunderstanding of transport in quantum wires is critical for nanocircuitry. Thus, the resultsof this proposal will be important for the multi-disciplinary nanoscience community. Theeducation component will advance discovery and understanding of nanoscience whilepromoting teaching, training and learning at different levels and broaden the participationof underrepresented groups.Non-technical abstract:The research focus is on the fundamental properties of materials in confined geometries as are found on the nanoscale. At these scales the theories we usually use have to be modified to account for confinement and this brings issues like disorder and interactions between electrons to the forefront. The research will study these fundamental issues that may form the basis for future nanoscale devices (nanoelectronics). The principal investigator will develop and teach an introductory course on nanoscience for college freshmen. He will also participate in outreach to high school students through the internet and in person. Research results will be integrated into course material.