Theoretical Problems in Condensed Matter and Statistical Physics

目标和智力价值。根据这一奖项开展的研究将提高我们对凝聚态和统计物理中各种现象的理解。其中一些工作将试图解释现有实验中令人费解的结果。其他工作将致力于改进计算技术，理解现有理论模型的更广泛后果，或者建议对理论想法进行新的实验测试。这两种方法对于该领域的持续发展都很重要。该项目将通过其对教育的贡献以及通过开发能够对物理学的其他分支以及化学、材料科学和工程等相关领域产生影响的理论方法来产生更广泛的影响。将通过培训研究生和博士后研究员来促进教育。这位首席研究员还为一个在线期刊俱乐部做出了贡献，该俱乐部的目的是提高人们对凝聚态物理学令人兴奋的新发展的认识。他还通过在暑期学校的讲座，以及在教育机构的顾问委员会和会议上的服务来促进教育。根据这一提议，很大一部分研究将涉及传导电子被限制在一个或多个方向的系统的性质，以及发生在边界或界面上的现象。例如，场效应晶体管中的电子被捕获在界面上，可以被描述为一个二维电子系统。这样的系统在低温下的外加磁场中表现出特别丰富的行为。赠款下的一组项目将侧重于最近在这些系统中发现的由外加微波辐射引起的表面零电阻状态。目前最有希望的解释假设，辐照样品中的电子自发形成具有大静电场和循环电流的磁区，零电阻现象可以通过分隔磁区的壁的运动来解释。这里的研究将探索样品中的残余不均匀或其他无序将如何影响形成的磁畴的图案，以及倾向于钉扎磁畴壁的机制将如何影响测量的电学性质。其他研究将涉及强磁场中的二维电子系统的一些现象，统称为量子霍尔效应。其中一个项目将探索无序在特殊量子霍尔态中的作用，其激发服从奇异的非阿贝尔统计，这可能在量子计算中具有独特的潜力。另一个项目将专注于双层系统，在某些条件下，它可以进入层之间具有强烈相关性的相干态。在这种情况下，两层中符号相反的电流可以非常容易地流动，类似于电流在超导体或超流体中的流动，而两层中的对称电流只能作为霍尔电流流动，垂直于面内电场。层与层之间的电子隧穿在低电压下出现一个大的电导峰，这在某种程度上类似于超导体中的约瑟夫森隧穿现象，但人们对峰的高度和宽度等方面知之甚少。该项目将研究不同类型的无序和样品几何结构如何影响这些实验的结果。一维电子系统，除了其他地方，出现在碳纳米管和特殊的半导体结构中，具有许多独特的性质。最近的实验显示，当导线一部分中的电子密度降至临界值以下时，会出现特殊的行为，这表明低密度区域和高密度区域之间形成了自发屏障，该项目将试图解释这一点。计算方法将包括Hartree-Fock和密度泛函方法，以及一维玻色化。其他项目将研究自旋和自旋输运的动力学，包括自旋轨道效应、半导体、金属和混合结构。这也是一个具有基本未解问题和潜在技术应用的主题领域。

Goals and Intellectual Merit. Research to be carried out under this award will improve our understanding of a variety of phenomena in condensed matter and statistical physics. Some of the work will try to explain puzzling results from existing experiments. Other work will aim to improve calculational techniques, to understand the wider consequences of existing theoretical models, or to suggest new experimental tests of theoretical ideas. Both these approaches are important for continuing advances in the field.Broader Impact. The project will have broader impact through its contributions to education, and by developing theoretical approaches that can have impact in other branches of physics and in related fields of chemistry, materials science, and engineering. Education will be promoted through the training of graduate students and postdoctoral fellows. The principal investigator also contributes to an online journal club, whose purpose is to increase awareness of exciting new developments in condensed matter physics. He has also furthered education through lectures at summer schools, and through service on advisory boards for educational institutions and conferences.Projects. A large portion of the research under this proposal will concern properties of systems where conduction electrons are confined in one or more direction, as well as phenomena that occur at boundaries or interfaces. For example, electrons in a field effect transistor are trapped at an interface, and may be described as a two-dimensional electron system. Such systems exhibit particularly rich behavior in applied magnetic fields at low temperatures. One set of projects under the grant will focus on the recently discovered occurrence, in these systems, of a state of apparently zero electrical resistance that is induced by applied microwave radiation. The most promising current explanations hypothesize that electrons in the irradiated sample spontaneously form domains with large static electric fields and circulating currents, and that the phenomenon of zero resistance can be explained by motion of the walls separating domains. Research here will explore how residual inhomogeneities or other disorder in a sample will affect the pattern of domains that form, and how mechanisms that tend to pin domain walls will affect the measuredelectrical properties.Other research will concern some of the phenomena involving two-dimensional electron systems in strong magnetic fields, known collectively as quantum Hall effects. One project will explore the role of disorder in special quantum Hall states with excitations obeying exotic non-abelian statistics, which may have unique potential for quantum computation. Another project will focus on double layer systems, which, under certain conditions, can enter a coherent state with strong correlations between the layers. In this state, electrical currents of opposite sign in the two layers can flow very easily, analogous to current flow in a superconductor or superfluid, while symmetric currents in the two layers can flow only as a Hall current, perpendicular to an in-plane electric field. Electrons tunneling between the layers show a large conductance peak at low voltages, which is in some ways analogous to the Josephson tunneling phenomenon in superconductors, but aspects such as the height and width of the peak are poorly understood. The project will examine how different types of disorder and sample geometry may affect the results of these experiments.One-dimensional electron systems, which occur, among other places, in carbon nanotubes and in special semiconductor structures, have many unique properties. Recent experiments showed peculiar behavior when the density of electrons in a portion of the wire was reduced below a critical value, suggesting that a spontaneous barrier was formed between the low- and high-density regions, which the project will try to explain. Calculational methods will include Hartree-Fock and density-functional methods, as well as one-dimensional bosonization.Other projects will examine the dynamics of spin and spin transport, including spin-orbit effects, insemiconductors, metals, and hybrid structures. This is also a subject area with fundamental unanswered questions and potential technological applications.