Non--Perturbative Interaction Effects in Disordered and Granular Metals

该奖项支持强相关电子材料领域的理论研究和教育。电子-电子相互作用对无序体系的输运和热力学性质有着显著的影响。这种效应在降维的系统中尤其明显。虽然微扰效应（发生在相对较弱的无序和高温下）已经被很好地理解，但对于实验学家和理论家来说，强无序或低温系统仍然是智力上的挑战。PI的目的是解决强无序和强关联的孪生问题与量子场论的非微扰方法。瞬时子方法在量子点库仑阻塞的研究中取得了丰硕的成果。在工作的第一阶段，PI将扩展他的Keldysh非线性sigma模型方法，以研究由大量强连接点（颗粒）组成的颗粒阵列。开发的技术将被应用到一般的无序系统。该研究的目标是可靠地描述强无序金属的低温性质，包括最近在实验中观察到的明显的玻璃态行为。该奖项的更广泛影响主要是教育性的。本科生（包括参加NSF赞助的REU和暑期学生项目的学生）将参与研究活动。该项目还将涉及至少一名全日制研究生，预计将积极参与指导本科生研究。高级固态课程将直接受益于研究活动的结果。该奖项还将促进与工业界的互动（计划为工业研究人员举办研讨会和可能的小型课程），以及与来自德国、以色列、日本和俄罗斯的科学家的国际合作。工作成果将在科学出版物、国家和国际会议及其会议记录中广泛传播。另一个传播途径是通过研究生暑期学校，如Les-Houches。该奖项支持理论研究和教育，以解决具有强相关电子的无序材料的挑战性问题。电子运动中的相关性来自于电子之间的强相互作用。虽然理解具有规则原子排列的强相关材料本身是一个具有挑战性的问题，但强相关和原子无序配置的组合是一个非常困难的问题。PI将使用理论凝聚态物理学的先进方法来解决这个问题，从考虑颗粒系统开始。实验揭示了无序和强关联系统中有趣而又知之甚少的现象。对这些的理解可能提供理解被认为不会发生在无序二维系统中的金属态的明显实验观察和最近在一些实验中观察到的明显玻璃态行为的关键。 该奖项的更广泛影响主要是教育。本科生（包括参加NSF赞助的REU和暑期学生项目的学生）将参与研究活动。该项目还将涉及至少一名全日制研究生，预计将积极参与指导本科生研究。高级固态课程将直接受益于研究活动的结果。该奖项还将促进与工业界的互动（计划为工业研究人员举办研讨会和可能的小型课程），以及与来自德国、以色列、日本和俄罗斯的科学家的国际合作。工作成果将在科学出版物、国家和国际会议及其会议记录中广泛传播。另一个传播途径是通过研究生暑期学校，如Les-Houches。

This award supports theoretical research and education in the area of strongly correlated electron materials. Electron-electron interactions have a dramatic effect on transport and thermodynamic properties of disordered systems. The effect is especially pronounced in systems with reduced dimensionality. While perturbative effects (taking place at relatively weak disorder and high temperature) are rather well understood, strongly disordered or low-temperature systems continue to be intellectually challenging for both experimentalists and theoreticians. The PI aims to address the twin problem of strong disorder and strong correlation with non-perturbative methods of quantum field theory. Instanton approaches have been fruitful for the study of the Coulomb blockade in quantum dots. In the first phase of the work, the PI will extend his Keldysh nonlinear sigma model approach to study granular arrays consisting of a large number of strongly connected dots (grains). The developed techniques will then be applied to generic disordered systems. The goal of the research is to describe reliably low-temperature properties of strongly disordered metals, including an apparent glassy behavior recently observed in experiments.Broader impacts of the award are primarily educational. Undergraduate students (including those participating in the NSF sponsored REU and summer-student programs) will be involved in the research activities. The project will also involve at least one full-time graduate student, who is expected to actively participate in directing undergraduate research. The upper level solid-state courses will directly benefit from the results of the research activity. This award will also facilitate interactions with the industry (seminars and possibly mini-courses are planned to be given for industrial researchers) as well as international collaboration with scientists from Germany, Israel, Japan and Russia. Results of the work will be disseminated broadly in scientific publications, national and international conferences and their proceedings. An additional venue of dissemination will be through graduate summer-schools, such as Les-Houches.%%%This award supports theoretical research and education to tackle the challenging problem of disordered materials with strongly correlated electrons. Correlations in the motion of electrons arise from strong interactions between electrons. While understanding strongly correlated materials with a regular arrangement of atoms is a challenging problem in and of itself, the combination of strong correlation and a disordered configuration of atoms is a very difficult problem. The PI will use advanced methods of theoretical condensed matter physics to attack this problem starting from a consideration of granular systems. Experiments have revealed interesting and poorly understood phenomena in disordered and strongly correlated systems. The understanding of these may provide the key to understanding apparent experimental observations of a metallic state thought not to occur in disordered two-dimensional systems and an apparent glassy behavior recently observed in a number of experiments. Broader impacts of the award are primarily educational. Undergraduate students (including those participating in the NSF sponsored REU and summer-student programs) will be involved in the research activities. The project will also involve at least one full-time graduate student, who is expected to actively participate in directing undergraduate research. The upper level solid-state courses will directly benefit from the results of the research activity. This award will also facilitate interactions with the industry (seminars and possibly mini-courses are planned to be given for industrial researchers) as well as international collaboration with scientists from Germany, Israel, Japan and Russia. Results of the work will be disseminated broadly in scientific publications, national and international conferences and their proceedings. An additional venue of dissemination will be through graduate summer-schools, such as Les-Houches.***