Disorder and the Quantum Hall Effect

9616880 Shklovskii This grant to a senior, distinguished theorist involves study of interplay between disorder and coulomb interaction, a subject to which he has made several seminal contributions. This grant consists of three related projects, all involving low to moderate magnetic fields. In one, the PI proposes to study the transport properties of a crystal of charged bubbles (clusters of electrons) that has recently been proposed as a possible ground state of a layer of electrons in low magnetic fields. In another project, there are plans to study the crossover between the moderate magnetic field regime represented by quantum Hall effect and the oscillations in resisitivity at low fields, the Shubnikov-de Haas oscillations. Finally, there is a project to study quantum version of the Coulomb gap, expected to be present during a metal-insulator transition or near a transition between the two plateaus in the quantum Hall effect regime. %%% This grant to a senior, distinguished, theoretical physicist is to study the subtle and complex properties of a thin layer of electrons. This PI is well known for his seminal contributions to this subject. In this grant, the work will concentrate on the effects of impurities and interaction between electron on electrical current in the presence of a moderate magnetic field. All of the projects involve sophisticated state-of-the-art mathematical machinery and includes further development of these mathematical tools.