Study of the coherent states of the two-dimensional electron gas in graphene

石墨烯中二维电子气相干态的研究 石墨烯是石墨的原子层，在过去的几年里已经成为材料科学和凝聚态物理学的星星。从技术的角度来看，它的强度，柔韧性，透明度，高和可控的导电性都为探索其用于高速电子电路提供了强大的驱动力。对于基础研究，石墨烯是有趣的，因为它的电子行为方式与传统的二维电子气（2DEG）完全不同：它们是无质量和手性的，具有相对论色散关系，价带和导带之间的间隙为零。建议的研究的目的是研究的光学和电学输运性质的2DEG在石墨烯中的电子之间的库仑相互作用时，考虑到和强垂直磁场施加到样品。在非常低的温度和具有非常低的无序的样品中，磁场和库仑相互作用的组合可以导致形成多体状态，其中2DEG中的电子集体行为。这种状态通常具有新的传输特性，可能需要新的物理模型来理解。它们还可能具有光学或电子特性，这些特性可能导致制造新的微电子器件。我们改变石墨烯中的2DEG的参数，以找到不同的多体状态，并研究它们的性质，如磁场，电子密度，或石墨烯的能带结构被修改。能带结构的改变自然发生在由多于一层石墨烯（例如双层和三层石墨烯）组成的系统中。

Study of the coherent states of the two-dimensional electron gas in graphene Graphene, an atomic layer of graphite, has become over the past years a star in material science and condensed matter physics. From a technological point of view, its strength, flexibility, transparency, high and controllable conductivity all provide a strong drive to explore its use for high-speed electronic circuits. For fundamental research, graphene is interesting because its electrons behave in a way which is radically different from that in a conventional two-dimensional electron gas (2DEG): they are massless and chiral with a relativistic dispersion relation and zero gap between valence and conduction bands. The objective of the proposed research is to study the optical and electrical transport properties of the 2DEG in graphene when Coulomb interaction between electrons is taken into account and when a strong perpendicular magnetic field is applied to the sample. At very low temperature and in samples with very low disorder, the combination of magnetic field and Coulomb interaction can lead to the formation of many-body states where electrons in the 2DEG behave collectively. Such states often have novel transport properties that may require new physical models for their understanding. They may also have optical or electronic properties that could lead to the fabrication of new microelectronic devices. We vary the parameters of the 2DEG in graphene to find the different many-body states and study their properties as the magnetic field, the electronic density, or the band structure of graphene is modified. A modification of the band structure occurs naturally in systems consisting of more than one layer of graphene such as bilayer and trilayer graphene.