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

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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. *****