Phenomenology of Correlated Electron Systems

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0081039JoyntSome of the deepest problems in science have to do with the motion of electrons, the carriers of electricity. Their behavior is governed by quantum many-body theory, whose laws often lead to strange and beautiful consequences. The understanding of these particles, and the resulting control that we have over them, underlies a wide range of technology from chemical engineering to computers.A particularly difficult challenge for solid-state physics is to understand the behavior of groups of electrons under special circumstances: when they act collectively because of their mutual interactions. This is a much deeper problem than the individual behavior of isolated electrons. The understanding of the latter is relatively well developed and forms the basis for today's electrical technology. The understanding of collective behavior will be important for the technology of tomorrow. The research in thi sgrant attacks this problem from two different directions: experimental analysis and fundamental calculations.In order to understand collective, or correlated, behavior of electrons, we must have well-developed tools for gathering information about them. One very important such tool is the photoelectric effect, which probes electron behavior by looking at the electrons that emerge from a metal when light is shown on it. In order for this experiment to give accurate information about the metal, we must understand the various ways that the electron can slow down and lose energy before it is detected. Calculations of thi senergy loss, and the resulting experimental signatures, i sone focus of the research.A second focus is to calculate the energies of electrons in very small structures called quantum dots. These structures are sure to be important in future computer technology, as miniaturization of chips and memory elements continues. Current theory does not furnish a good account of the motion of electrons in these structures. Their energy levels are puzzling: we even lack a rough, statistical description. We will use an algorithm based on biological ideas, the so-called gentic algorithm, to calculate these levels. This will be the first time such ideas have been applied specifically to the quantum nature of these particles.One very important example of collective behavior of electrons is superconductivity: the ability of electrons to carry electrical current as a group. Important new classes of these materials have been discovered in recent years, and their properties are novel and, in many cases, poorly understood. The theoretical research in this area, a continuation of a long-standing effort, focuses on understanding numerous experiments and constructing models that combine the phenomena of superconductivity and magnetism.***