Correlated Electron Transport in One-Dimensional Channels - The object of this project is to build a theoretical structure within which to treat quantum transport for a system with interacting electrons, in particular for narrow channels formed in gated semiconductor heterostructures. Coulomb repulsion between electrons becomes crucially important at low electron density, resulting in long-range interactions and correlated states. Two models for a strongly correlated system of electrons will be investigated. In the first model fluctuations of the electrostatic potential that forms the channel within the inversion layer is taken as much smaller than the electron-electron interaction. The second model will take account of strong fluctuations in the potential and the resulting formation of almost isolated quantum dots. These models will be compared with experimental results. %%% Recent progress in fabrication of semiconductor structures, including electron beam lithography and MBE growth on vicinal surfaces, has allowed the systematic experimental study of quantum transport on submicron length scales. Existing theories accurately describe the case where the electrons in a narrow channel move with very little scattering, and the opposite case where the electrons are frozen tightly in place. There is, however and intermediate regime where a single sample can be changed from a metal to an insulator simply by changing the electron density. This much more interesting regime cannot be treated using conventional models, because they do not include electron-electron interactions properly. This research project proposes to develop models for this intermediate transition regime. Such understanding is quite important, as this class of effects have been proposed as the basis for the next generation of ultra-small electronic devices.
