Theoretical Problems in Condensed Matter and Statistical Physics

Harvard University, Cambridge MA

Investigators

Abstract

0233773 Halperin Theoretical research carried out under this grant 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. The project will have educational impact through the training of graduate students, undergraduates and postdoctoral fellows. The Principal Investigator is also involved in efforts to develop presentations to the general public, which could benefit from this research. A large portion of the research will concern properties of systems where conduction electrons are confined in one or more directions. As an important example of such a system, the electrons in a field-effect transistor are trapped at a semiconducting interface, and may be described as a two-dimensional electron system. A number of surprising phenomena, known collectively as quantum Hall effects, have been discovered in two-dimensional electron systems in strong magnetic fields at low temperatures. Recently, experiments have been carried out on systems with two parallel two-dimensional electron systems, coupled by the Coulomb interactions between electrons in different layers. Research under this grant will develop improved theories of the various states that can occur in such systems, including weakly and strongly coupled phases, and phases where the electron density may vary periodically in space on the scale of 100nm. Drag experiments, where current in one layer produces a voltage in the second layer, show puzzling results in quantum Hall systems, which this research proposes to explain. The research will also try to improve the understanding of experiments that measure the conductance arising from electrons that tunnel through the barrier between the two layers. Other work will try to understand shot noise measured in single-layer quantum Hall systems when current passes through a series of narrow constrictions. Another research area will be the study of one-dimensional electron systems, which can occur in carbon nanotubes, or can be fabricated out of two-dimensional electron systems in semiconductors. Previous analyses of the effects of electron-electron interactions on tunneling between parallel one-dimensional wire segments will be extended to more general ranges of experimental parameters. Other work will try to understand drag experiments with parallel wires, and will explore phenomena in semiconductor nanowires. Another research topic will explore generalizations of the Kondo effect, where repeated flips of the spin of a localized electron produce peculiar effects in electrical transport at low temperatures. Generalizations include situations where changes in the position of a localized electron, rather than its spin, give rise to anomalous transport effects: and situations where the coupled motion of several interacting electrons is crucial. Other theoretical work will explore aspects of sound propagation and of NMR measurements in fluid-containing rock formations, which could have significance for oil well management. %%% Theoretical research carried out under this grant 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. The project will have educational impact through the training of graduate students, undergraduates and postdoctoral fellows. The Principal Investigator is also involved in efforts to develop presentations to the general public, which could benefit from this research. ***