Electron-electron interaction effects in the optical and transport properties of 2D materials beyond graphene

This Thesis studies optical, plasmonic, and transport phenomena in two-dimensional materials. In particular, optical and plasmonic properties in twisted bilayer graphene are analyzed in the first part of the Thesis, whereas transport phenomena in twodimensional topological insulators are left for the second part. A common element of the physical systems studied here are electron-electron interactions, whose presence is pivotal for many of the results presented. The first Chapter of the manuscript is devoted to a review and critical analysis of the experimental results that motivated our work. Among these results, I emphasize recent experimental work carried out at ICFO on MIT samples on the plasmonic properties of twisted bilayer graphene whose theoretical interpretation was accomplished mostly thanks to the original theory presented in this Thesis. The first Chapter is also devoted to present some of the necessary theoretical concepts and tools forming the basis of this manuscript. The second Chapter of the thesis presents a theory of twisted bilayer graphene, an atomically-thin heterostructure which in early 2018 was showed to host a plethora of exotic quantum phases of matter. This Chapter also includes a technical Section where the details of the numerical codes developed for our study of twisted bilayer graphene are thoroughly discussed. These numerical codes are planned to be fully released and openly available for the scientific community in the near future. The third Chapter contains original results on the optical and plasmonic properties of twisted bilayer graphene. These results are obtained for a large variety of different parameter configurations, in the spirit of giving as much information as possible for a material (twisted bilayer graphene) whose actual physical properties are to a large extent still unknown. This Chapter is concluded by the presentation of preliminary results on the density-density response function of twisted bilayer graphene, which is essential to understand its dielectric properties, and hence how and how much the electron-electron interactions are screened. The fourth Chapter is about the theory of two-dimensional topological insulators, a class of materials hosting very interesting transport phenomena that are related to to the topological nature of their non-interacting bands and eigenstates. A Section of this Chapter is also devoted to the theory of ballistic electron transport, which is essential to understand many properties of two-dimensional topological insulators. In the fifth and last Chapter of the Thesis, we present an original result on the interplay between electron-electron interactions and localized defects in two-dimensional topological insulators. The theory presented in this Chapter provides a straightforward conceptual framework to explain experimental results on the transport properties of two-dimensional topological insulators, especially those in atomically thin crystals, plagued by short-range edge disorder.