Theoretical Problems in Condensed Matter and Statistical Physics

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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.