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

石墨烯中二维电子气的相干态研究 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中的明星。从技术角度来看，它的强度、灵活性、透明度、高导电性和可控性都为探索其在高速电子电路中的应用提供了强大的动力。对于基础研究来说，石墨烯很有趣，因为它的电子的行为方式与传统的二维电子气(2DEG)完全不同：它们是无质量的手性的，具有相对论色散关系，价带和导带之间的零隙。这项研究的目的是研究在考虑电子间库仑相互作用和施加强垂直磁场的情况下，石墨烯中二维电子气的光学和电学输运性质。在极低温度和极低无序度的样品中，磁场和库仑相互作用的结合可以导致二维电子集体行为的多体态的形成。这种状态通常具有新的传输特性，这可能需要新的物理模型来理解它们。它们还可能具有光学或电学特性，这可能导致制造新的微电子设备。我们通过改变石墨烯中二维电子气的参数来发现不同的多体态，并研究了随着磁场、电子密度或石墨烯能带结构的改变而产生的多体态的性质。能带结构的改变自然发生在由一层以上的石墨烯组成的系统中，例如双层和三层石墨烯。

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.