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

当一种电子气体在极低的温度下被限制在量子阱的最低能态时，它的行为就像它实际上是二维的一样。维数的减少增加了电子间库仑相互作用的作用。当在系统中加入一个垂直于二维电子气体（2DEG）平面的强磁场时，电子的能量进一步量子化为朗道能级。当电子填满这些能级时，实验观察到丰富多样的电子状态。这些状态中最杰出的是发生在朗道能级的整数和一些分数填充处的劳克林液态，在这些状态中，电子集体聚集在一起，产生霍尔电导的精确量子化。在本研究项目中，我们研究了发生在朗道能级整数填充之外的其他2DEG集体态：Wigner晶体、Skyrmion晶体、条纹相和气泡相。我们还观察了在双量子阱结构和单层石墨中形成的2DEG中出现的类似状态。我们研究了这些态的能量学，以及它们的集体激发和实验特征。我们试图理解量子约束、库仑相互作用和量子涨落如何共同赋予这些态独特的输运和电子性质。

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.