Theoretical Studies of the Quantum Hall Effect and Nonlinear Mesoscopic Transport

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This award supports theoretical research to study fundamental properties of the integer and fractional quantum Hall effects, and to study mesoscopic transport. The PI has developed an ensemble density functional theory approach to study the fractional quantum Hall effect in large inhomogeneous systems such as quantum dots. The theory enables the inclusion of electron correlations, spin, arbitrary confinements, finite layer thickness, Landau-level mixing and finite temperature. The ensemble density functional theory will be used to study the properties of quantum dots in large magnetic fields. Comparison with addition spectrum, magnetoluminescence, and tunneling experiments will show how measured features result from changes in electron density, correlation state, and spin and edge structures. The ensemble density functional theory will be further developed to include the off-diagonal long-range order of the fractional quantum Hall effect and then applied to quantum dots. The PI also plans to study the edge modes of quantum Hall systems. The focus of this research is on recent experimental data for which a Luttinger liquid description works when it should not. The PI intends to test whether this is a consequence of correlations in the lowest Landau level. The ensemble density functional theory will be used to investigate edge structures under different conditions in dots.Another thrust of the PI's research involves a transport formalism that he developed for steady-state mesoscopic systems which is valid beyond the linear response regime. The formalism will be applied to study specific non-ideal systems, including quantum point contacts. The PI plans to explore model systems comparing his approach to traditional approaches, such as nonequilibrium Green's functions, with the aim of gaining insight into steady-state highly nonequilibrium statistical mechanics including the role of boundary conditions. %%%This award supports theoretical research on quantum dots in high magnetic fields and in transport properties of mesoscopic devices. The research will use state-of-the-art methods that can include materials specific properties and specific geometries to study possible new electronic states that are believed to occur in high magnetic fields. This research is fundamental, but lays groundwork that may be important for developing the electronic device technologies of the 21st century. The proposed work provides educational opportunities for training the next generation of condensed matter theorists.***