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

这个CAREER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依赖于时间的场和其他远离平衡的条件下工作，因此对纳米尺度上的非平衡输运的理解至关重要。因此，量子线的现实描述提出了电子相互作用存在下的非平衡效应的难题。固体总是含有杂质，因此如果不理解无序和相互作用的相互作用，就不可能理解介观输运。该研究将采用系统的分析和数值方法相结合，以调查量子线中远离平衡输运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。本研究将围绕以下几个问题展开：1. Luttinger液体中的非平衡输运。在棘轮效应中，直流电流是由空间非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。现有的棘轮效应的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。然而，电子相互作用是显着的，并导致在量子线中的Luttinger液体的形成。本论文的研究工作将包括利用Keldysh技术、玻色化、重整化群、大N平均场方法和数值方法对Luttinger液体中的棘轮效应进行系统的研究.远离平衡态的自旋输运。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。本研究将包括对Luttinger液体中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。拟议的研究将结合联合收割机的方法，把二维电子气作为一个系统的相互作用的量子线与玻色化程序和方法发展的软物质系统理论与淬火无序。这种方法可以帮助解决QHE高原过渡的问题。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;将与补助金相关的领域的最新发展整合到常规物理课程中;学生和博士后参与研究和相关活动，如期刊俱乐部;以及扩展到普罗维登斯市中心的高中。基于互联网的高中水平的教程将准备新生课程的基础上，在智力的理由，拟议的研究将推进有关强相关的电子系统的知识。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是一个充满困惑和惊奇的领域。这一领域的进展具有根本重要性。本文的研究将对远离平衡态量子多体系统的涌现领域的研究有所裨益。拟议的工作将采用低维电子系统和软凝聚态之间的类比，从而弥合硬物质和软物质物理之间的现有差距。拟议的研究也将产生更广泛的影响。对量子线中的输运的理论理解对于纳米电路是至关重要的。因此，这一建议的结果将是重要的多学科纳米科学界。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有限几何形状材料的基本属性。 在这些尺度上，我们通常使用的理论必须修改以解释限制，这将电子之间的无序和相互作用等问题带到了最前沿。 该研究将研究这些可能构成未来纳米器件（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和教授纳米科学入门课程。 他还将通过互联网和亲自参加对高中生的宣传活动。 研究成果将纳入课程材料。

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.