This coherent monograph describes and explains quantum phenomena in two-dimensional (2D) electron systems with extremely strong internal interactions, which cannot be described by the conventional Fermi-liquid approach. The central physical objects considered are the 2D Coulomb liquid, of which the average Coulomb interaction energy per electron is much higher than the mean kinetic energy, and the Wigner solid. The text provides a new and comprehensive review of the remarkable properties of Coulomb liquids and solids formed on the free surface of liquid helium and other interfaces. This book is intended for graduate students and researchers in the fields of quantum liquids, electronic properties of 2D systems, and solid-state physics. It includes different levels of sophistication so as to be useful for both theorists and experimentalists. The presentation is largely self-contained, and also describes some instructive examples that will be of general interest to solid-state physicists.

Consists of invited lecture series and contributed research papers presented at the International Advanced School in Statistical Physics held at Punjab University, Chandiqarh, India under the Indo French Program of Cooperation in Science and Technology. Examines current studies of static and dynamical properties of liquids through time correlation function, computer simulation and neutron scattering experiments. Various Coulomb systems are introduced, with examples in one, two, and three dimensions provided. Small angle neutron scattering data from polydispersed random media are reviewed. Final sections discuss quantum theories of diffusion of localized and Bloch impurities in solids, chaos and turbulence, the spin glasses SK model and recent results on high temperature superconductors.

This thesis covers many-body liquids and solids occurring in two-dimensional electron systems (2DESs) confined to GaAs and AlAs quantum wells subjected to a large perpendicular magnetic field and cooled to very low temperatures. In GaAs 2DESs, we systematically explored the fractional quantum Hall liquid energy gap. Then, the Wigner solid and fractional quantum Hall liquid competition was investigated in AlAs 2DESs. Also, the very low-disorder GaAs 2DESs allow us to probe the thermal melting of bubble phases, a type of Wigner solid.In the first part of this thesis we report a systematic experimental study that incorporates very high-quality 2DESs confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the fractional quantum Hall energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that take into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below calculated values, but as the electron layer thickness increases, experiments and calculations are in better agreement. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.Next, the fate of the ground state of a 2DES at very low Landau level filling factors (v) where interaction reigns supreme was explored. We report experimental data for a new 2DES where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the 2D electrons in a large range of filling factors near $\\simeq 1/3$ and $\\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.In the latter part of this thesis, we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram for the transition from bubble to liquid phases for Landau level filling factors 4 ≤ v ≤ 5.