Electronic Properties of Nanostructures

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This is a theoretical project in the area of mesoscopic physics. The electronic properties of nanoscale structures will be investigated including:Superconductivity in thin wires. When the cross-section of a wire is as small as a few square nanometers, the wire is expected to lose its superconducting properties. The critical Josephson current in such wires will be studied, as well as the dependence of the current on the applied phase difference. The research will then be extended to study other properties of superconducting nanowires, including their current-voltage characteristics. Comparisons will be made to experiments.Propagation of interacting one-dimensional electrons in quantum point contacts. Unlike conventional Luttinger liquid theories, this work will involve scattering off a smooth potential barrier. Both conventional perturbation theory and bosonization techniques will be used. This work is expected to advance our understanding of electron transport in mesoscopic systems, especially semiconductor heterostructures, and provide theoretical understanding of recent experimental results. Decay of metastable states in double barrier resonant tunneling structures and superlattices. The understanding of the decay time is important for potential applications of the bistability features of these devices. This work will involve conventional kinetic theory techniques, such as Fokker-Planck equations, as well as modern approaches developed for quantum field theory problems.%%%This is a theoretical project in the area of mesoscopic physics. The electronic properties of nanoscale structures will be investigated. This is very important from a fundamental perspective in order to understand th ebehavior of electrons in very small structures. It is also at the very foundation of applications of nanoelectronics to devices affecting our everyday life.***