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. ***
