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

石墨烯中二维电子气体相干态的研究****石墨烯是石墨的原子层，近年来已成为材料科学和凝聚态物理学的明星。从技术的角度来看，它的强度、柔韧性、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，石墨烯很有趣，因为它的电子行为方式与传统的二维电子气体（2DEG）完全不同：它们是无质量的、手性的，具有相对论色散关系，价带和导带之间的间隙为零。本研究的目的是研究考虑电子之间的库仑相互作用和施加强垂直磁场时石墨烯中2DEG的光学和电输运性质。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多体态的形成，其中电子在2DEG中具有集体行为。这种状态通常具有新的输运性质，可能需要新的物理模型来理解。它们也可能具有光学或电子特性，这可能导致制造新的微电子设备。我们通过改变石墨烯中2DEG的参数，找到不同的多体态，并研究它们在磁场、电子密度或石墨烯带结构改变时的性质。在由多层石墨烯组成的系统中，如双层和三层石墨烯，自然会发生能带结构的修饰。******************

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.******************