Electronic properties of the collective states of a two-dimensional electron gas in a strong magnetic field

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Electronic properties of the collective states of a two-dimensional electron gas in a strong magnetic fieldWhen a gas of electrons is confined, at very low temperature, into the lowest-energy state of a quantum well, it behaves as is it was effectively two-dimensional. This reduction in dimensionality increases the role of the coulombian interaction between electrons. When a strong magnetic field, perpendicular to the plane of the two-dimensional electron gas (2DEG) is added to the system, the energy of the electrons is further quantized into Landau levels. As the electrons fill these levels, a rich diversity of electronic states are observed experimentally. The most illustrious of these states are the Laughlin liquid states occurring at integer and some fractional fillings of the Landau levels where the electrons collectively ensemble themselves to produce an exact quantization of the Hall conductance. In this research project, we study other collective states of the 2DEG that occur away from the integer filling of the Landau levels: Wigner crystal, Skyrmion crystal, stripe and bubble phases. We also look at similar states that occur in the 2DEG formed in a double quantum well structure and in single layers of graphite. We study the energetics of these states as well as their collective excitations and experimental signature. We try to understand how the quantum confinement, coulombian interactions and quantum fluctuations conspire to give to these states their unique transport and electronic properties.