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

这个职业奖将低维导体的研究与大学和高中学生的教育活动结合起来。由于未来的纳米器件将在时间相关的场和其他远离平衡的条件下工作，因此了解纳米尺度上的非平衡输运至关重要。因此，对量子线的现实描述提出了电子相互作用下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。研究将采用系统分析和数值方法相结合的方法来研究量子线中非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。研究将集中在以下几个问题上：1。卢廷格液体中的非平衡输运。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。现有的棘轮效应理论研究主要集中在费米-液体系统和非相互作用电子的简化模型上。然而，电子相互作用是重要的，并导致在量子线卢廷格液体的形成。建议的研究将包括使用Keldysh技术、玻色子化、重整化群、大n平均场方法和数值方法对luttingerliquid中的棘轮效应进行系统调查。远离平衡的自旋输运。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研究产生自旋电流的可能方法。提议的研究将包括对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。最近关于分数电荷准粒子的干涉和隧穿实验提出了一些标准方法无法回答的准粒子输运的基本问题。提出的研究将把一种将二维电子气体作为相互作用量子线系统的方法与玻色子化过程和具有淬火无序的软物质系统理论中发展的方法相结合。该方法有助于解决QHE高原过渡问题。教育活动将包括主要针对新生的纳米科学入门课程的开发；将与赠款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；并扩展到普罗维登斯市内的高中。在大一课程的基础上，将编写一个基于网络的高中水平的教程。在知识基础上，本研究将促进强相关电子系统的知识。量子力学的基本定律早已为人所知，但多体系统的涌现特性仍然构成了一个充满谜题和惊喜的领域。这一领域的进展具有根本的重要性。所提出的研究将有利于新兴的非平衡量子多体系统领域。提出的工作将采用低维电子系统和软凝聚态物质之间的类比，从而弥合硬物质和软物质物理之间的现有差距。拟议中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纳米电路至关重要。因此，这一建议的结果将对多学科纳米科学界具有重要意义。教育部分将促进纳米科学的发现和理解，同时促进不同层次的教学、培训和学习，并扩大代表性不足群体的参与。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。在这样的尺度下，我们通常使用的理论必须进行修改，以解释约束，这就把电子之间的无序和相互作用等问题带到了最前沿。这项研究将研究这些可能构成未来纳米级器件（纳米电子学）基础的基本问题。首席研究员将为大学新生开发并教授一门纳米科学入门课程。他还将通过网络和亲自参加对高中生的宣传活动。研究成果将纳入课程教材。

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.