This award supports theoretical research in fundamental condensed matter physics. The Fermi-liquid description of weakly interacting quasiparticles has been remarkably successful as a framework for treating the properties of the electron fluids encountered in a wide variety of crystalline materials and solid state devices, even where the electron-electron interactions are quite strong, and the Fermi liquid parameters are strongly renormalized from their bare values. However, there are also many cases where the Fermi liquid approach qualitatively fails: systems in which whatever dispersing feature there are in the single particle spectral functions are overdamped in the sense that their widths are larger than their mean, or where there are phase transitions to broken symmetry states with temperature and energy scales comparable to microscopic electronic scales, or that exhibit macroscopic behaviors that are inconsistent with weakly interacting quasiparticles, such as finite resistance in a two-dimensional system in the low temperature limit, or metallic(increasing with increasing temperature) resistivities with magnitudes in excess of the Ioffe-Regel limit. Non-interacting electrons serve as the appropriate paradigmatic for well developed Fermi liquids, but simple, solvable models of strongly interacting electrons are few and far between. It is the principle purpose of the research envisaged here to obtain well controlled approximate, or even asymptotically exact solutions to simple models of strongly interacting electrons as a step in filling this void. More particularly, it is proposed to study models with purely repulsive interactions between electrons in which the existence of a superconducting state with a high transition temperature can be firmly established and the transition temperature reliably estimated. This study is relevant to elucidating the mechanism of high temperature superconductivity. On a more phenomenological level, it is proposed to study the effects of electronic micro-phase-separation, a common occurrence in strongly correlated "bad metals," on various macroscopic properties such as the optical conductivity and DC transport. While much of this effort is inspired by an attempt to understand the remarkable properties of the cuprate high temperature superconductors, applications of related ideas to low density electron gases in MOSFET's, and to other highly correlated electronic materials, such as transition metal oxides and the organic superconductors, are also planned.
There are, by now, many examples of highly correlated bad metals, where conventional approaches to the theory of electronic structure fail. Obtaining a simple, qualitative understanding of these materials is an intellectual question on par with, "What is a metal?" High temperature superconductivity is only one of the phenomena observed in such materials, but one of the most exciting.
This work will serve as a fertile source of research projects for students. The problems are well defined, and of direct experimental relevance, while at the same time involving mastery of a large number of methods of many body physics. %%% This award supports theoretical research on fundamental condensed matter physics. The topic is materials which exhibit strongly interacting electrons which produce effects, such as high temperature superconductivity, that are unable to be understood with current theory. A systematic procedure will be followed to develop and solve models, including experimental predictions, which will contribute to the understanding of these materials. As part of this project, students will be trained in modern techniques of condensed matter theory. ***
