Transport and optical properties of the interacting electron gas in Weyl semimetals and two-dimensional materials

摘要：电子气可以存在于不同的相中，这些相在很大程度上决定了主体材料的物理性质。这些相是由内部参数决定的，如材料的能带结构和尺寸，以及外部参数，如温度、密度和磁场或电场的存在。例如，当二维电子气体受到强垂直磁场时，电子的动能被量子化为简并朗道能级。通过改变这些水平的填充分数来改变气体的物理状态。自20世纪80年代以来，已经确定了几个相，如表现出整数量子霍尔效应的液态，或更复杂的相，如分数量子霍尔态或电子晶体和条纹相，这些相只能在考虑到电子之间的库仑相互作用时才能解释。这些复杂的状态是电子气体的集体状态。在这个提议中，我们感兴趣的是研究这些由于库仑相互作用和磁场共同存在而产生的集体态。我们想要研究它们在具有不同能带结构的量子材料中的出现，例如半导体量子阱中的二维电子气体和石墨烯（单层石墨）中的二维电子气体，或者Weyl半金属中的三维电子气体，一种像石墨烯一样具有拓扑能带结构的材料。我们想要研究当磁场变化时可能出现的电子气体的不同相，并推导出它们的单粒子激发、集体模式以及它们的电子和光学性质。我们的研究将提高我们对量子材料基本特性的理解，并有助于发现可用于构建新的微电子器件的特性。

Title: Transport and optical properties of the interacting electron gas in Weyl semimetals and two-dimensional materials Summary: An electron gas can exist in different phases that determine to a large extent the physical properties of the host material. These phases are determined by internal parameters such as the band structure and dimensionality of the material as well as external parameters such as temperature, density and the presence of a magnetic or electric field. For example, when a two-dimensional electron gas is subjected to a strong perpendicular magnetic field, the kinetic energy of the electrons is quantized into degenerate Landau levels. The physical state of the gas is modified by changing the filling fraction of these levels. Since the 1980s, several phases have been identified such as the liquid state that exhibits the integer quantum Hall effect or more complex phases such as the fractional quantum Hall states or the electron crystal and stripes phases that can only be explained if the Coulomb interaction between electrons is taken into account. These complex states are collective states of the electron gas. In this proposal, we are interested in studying these collective states that are due to the combined presence of the Coulomb interaction and a magnetic field. We want to study their occurrence in quantum materials that have different band structures such as the two-dimensional electron gas in semiconductor quantum well and in graphene (a single layer of graphite) or the three-dimensional electron gas in Weyl semimetals, a material like graphene that has a topological band structure. We want to study the different phases of the electron gas that are possible when the magnetic field is varied and derive their single-particle excitations, collective modes as well as their electronic and optical properties. Our study will improve our understanding of the fundamental properties of quantum materials and help in finding properties that could be exploited to build new microelectronic devices.