Since the discovery of graphene, the field of 2D materials has attracted increasing interest because of the novel and surprising properties that have been observed. Many of these arise from the interaction between electrons, causing them to collectively change their behavior. In this thesis, we study some of these effects, namely, electron hydrodynamics, correlated insulators in twisted bilayer graphene, and Majorana zero modes. In the first part of this thesis, we study electron hydrodynamics --- a transport regime wherein electrons behave as a fluid. This regime has been predicted to reduce resistance due to the collective flow of electrons. Although this can be predicted from kinetic theory in a simple electron gas, a fully ab initio theory is needed to gain insight into a wider range of materials. Here, we show how perturbation theory, the Boltzmann transport equation, and the Chapman-Enskog procedure can be used to derive a first principles expression for electron viscosity. We detail some of the intricacies involved in the computation of the electron viscosity and demonstrate an excellent agreement between the computational results and experimental findings. With this work, we can perform quantitative studies of electron hydrodynamics in a wide range of 2D materials. Twisted bilayer graphene, or TBG, consists of two layers of graphene rotated relative to one another. At specific angles of rotation, the bands become flat and the phase diagram shows areas of superconductivity and correlated insulating behavior. In the second part of this thesis, we propose a gate-defined wire in TBG and use proximity effects to identify the symmetry breaking order of the correlated insulator phases. We also show how this setup can be used to engineer Majorana zero modes, possibly without the need for an external magnetic field.
Ina Muggerud Sørensen (Mon,) studied this question.