My research involves the theoretical (both analytical and numerical) study of low-dimensional / nanoscale electronic and photonic systems, in and out of equilibrium. Nanoscale systems are immensely important as the basic building blocks of future electronic devices, which may lead, among other potential applications, to the eventual realization of scalable quantum computing. They can be fabricated using a variety of materials, including semiconductor heterostructures, metallic nanowires and nanograins (normal or superconducting), carbon-based materials (graphene, nanotubes, and buckyballs), the recently discovered topological insulators, and even conducting polymers and single molecules. Not less importantly, from a more fundamental perspective, nanoscale systems exhibit a variety of phenomena caused by strong electronic correlations, as well as their interplay with quantum interference effects and nonequilibrium behavior, all of which are central themes in current condensed matter research.
In particular, I am interested in the following systems:
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Semiconductor quantum dots and metallic nanograins, quantum impurity models, the Kondo effect
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Quasi 1D conductors (semiconducting and metallic nanowires, carbon nanotubes), Luttinger liquid theory
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Low dimensional superconductors and their applications in quantum computing and quantum simulation
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The Quantum Hall effect, topological insulators and superconductors
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Hydrodynamics of quantum fluids, Hall viscosity
