Theoretical investigations will be carried out on two-dimensional quantum semiconductor systems studying effects of disorder, finite temperatures and unique device structures with and without a magnetic field. The behavior of edges in the Wigner crystal regime in a strong magnetic field will be considered and a method for calculating relaxation, reconstruction and melting of the edge electrons under various circumstances will be studied. The consequences of transport and electromagnetic absorption of such effects will be considered. A detailed study of defects in the Wigner crystal will be undertaken using a variational wavefunction approach which should help determine the importance of quantum fluctuations and will be a first step in understanding both the melting transition and finite temperature transport. Edge states in the quantum Hall regime will be studied with emphasis on the effects disorder may have on the low-lying excitations of such systems. Finally, a careful study of the influence of potential inhomogeneities in a two-layer system on interplane tunneling will be undertaken. %%% This theoretical study will focus on the properties of a new state of matter associated with a gas of strongly interacting electrons confined to two-dimensions. Usually this state of matter is found at the semiconductor interface in a strong magnetic field. One possible outcome of this electron gas is to condense into a crystalline state, the Wigner crystal. The research will study the behavior of this Wigner crystal. Besides being of fundamental physical interest, there may be ramifications of this research on microelectronics.
