Theoretical Problems in Condensed Matter and Statistical Physics

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TECHNICAL SUMMARYThis award supports theoretical research and education focused on systems where conduction electrons are strongly confined in one or more directions. The research effort is motivated by experiment and encompasses a variety of intriguing phenomena. Apart from advancing understanding, a consequence of the research is to advance theoretical techniquesNanoscale semiconductor devices, known as double quantum dots, can be used to trap a pair of conduction electrons, and to manipulate their spins by applying electric potentials to adjacent gates in a prescribed sequence. The electron spins interact with nuclear spins in the host material, and can be used to manipulate the polarization of those spins. Recent experiments have produced some quite surprising results, which will be one focus of this research. The PI seeks to advance understanding of the non-equilibrium dynamics of this coupled system, a major challenge which could have practical as well as fundamental consequences. Two-dimensional electron systems, such as field effect transistors, exhibit very rich behavior in strong magnetic fields at low temperatures, including a remarkable set of phenomena known as the quantum Hall effects. When a system is in a quantized Hall state, it can carry electric currents along the sample edges, with almost no energy loss. However, if there is a sufficiently narrow constriction in the sample, electrons can tunnel from one edge to another, leading to electrical resistance. Two or more constrictions can lead to resistance that oscillates rapidly as a function of magnetic field strength or of voltages applied to insulated gates on the sample. Such oscillations can originate from quantum mechanical interference effects, from electron-electron interaction effects (?Coulomb blockade?) or a combination of the two. The PI aims to sort out the importance of these effects in existing and future devices. Analysis of these experiments should tell us about the nature of edge states in real samples as well as the fundamental physics of quantum Hall systems. Research will also focus on oscillations that have been seen as a function of source-drain voltage, and on the current-voltage characteristics of individual constrictions.Another set of projects will focus on the state of apparently zero electrical resistance induced by applied microwave radiation, which has been seen in two-dimensional electron systems at intermediate values of the magnetic field. A recent experiment using circularly polarized radiation found the microwave effect to be completely independent of the sign of the circular polarization, in contrast to all theoretical predictions. The project will try to understand this, as well as other puzzling observations. The project will also explore designs for testing a prediction that nonuniformity in the electron density can give rise, in the zero-resistance state, to time-dependent oscillations in the local electrostatic potential.Finally, the PI aims to analyze experiments in which an electron tunnels, with controlled momentum, into a very thin ?quantum wire? or into the edge of a two-dimensional electron system in a quantum Hall state. The experiments should give important insights into the physics of these systems, including collective effects due to electron-electron interactions.NON-TECHNICAL SUMARYThis award supports theoretical research and education that encompasses a variety of phenomena in condensed matter and statistical physics. This research is focused on phenomena that arise in systems where conduction electrons are strongly confined in one or more dimensions. The PI aims to explain puzzling results from existing experiments that involve structures of atoms the size of very large molecules so that the ?nanostructures? lie between being a material and an electronic device, and experiments involving electronic states of matter that arise when electrons are confined to a plane within a semiconductor structure and exposed to a very high magnetic field perpendicular to the plane, quantum Hall states. All these experiments probe fundamentally interesting phenomena in which the wave-like nature of electrons plays a crucial role. Phenomena like these appear and their understanding becomes increasingly important as the size of electronic circuit elements shrink to ever smaller dimensions at the pace of Moore?s law. Apart from the important role of advancing fundamental knowledge of the world around us, this research contributes to the intellectual foundations of new technologies that help to preserve the rapid advance of electronics technologies.