Theoretical Studies of the Quantum Hall Effect and NonlinearMesoscopic Transport

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9301433 Johnson This theoretical research will study fundamental transport and microscopic properties in the integer and fractional quantum Hall effects (IQHE and FQHE). A novel approach to transport in the IQHE has been developed and will be adapted to nonlinear mesoscopic transport and applied to the study of nonlinear time-independent and time-dependent effects in devices. In the IQHE this approach will be used to study current distributions and the breakdown of dissipationless IQHE, fundamental properties which are not presently well understood. The possibility of developing a novel tunable phonon or photon laser, based on the breakdown, will be studied. The FQHE research will include a detailed study of the properties and experimental consequences of edge excitations at complicated fractions, and an investigation of the appropriate description of bulk quasiparticle excitations. These are important to understand the microscopics of the FQHE. Finally, a method based on density functional theory will be developed which will provide a powerful numerical tool to study the properties of an inhomogeneous electron gas in a strong magnetic field. %%% The research conducted on this grant deals with one of the most important current problems in modern condensed matter physics. The research focuses on the properties of a new state of matter which is formed in a strong magnetic field at a semiconductor interface under certain conditions. This "two-dimensional electron gas" has many unusual properties. Besides being of fundamental interest, these properties may have application to new and novel electronic devices. The work will concentrate on nonlinear transport phenomena and a density functional formulation of the problem. These are topics which have not received a great deal of attention. ***