Hydrodynamics and plasmonics in two-dimensional materials

This Thesis is devoted to the study of two different aspects of electron behavior in two-dimensional materials, namely hydrodynamic electron transport and plasmon propagation. The Thesis is structured as follows. In Chapter 1 the main experimental facts that motivated our work on electron hydrodynamics and plasmonics are presented and critically discussed. Chapter 2 contains our main results on hydrodynamic electron transport. After deriving the basic equations of the electron hydrodynamics and discussing their limit of applicability, we use them to quantify the impact of two different transport coffcients, the shear and Hall viscosities of the electron liquid, on steady-state transport. Our results are used to propose experimental protocols that allow an experimental determination of these transport coeffcients. Chapter 3 deals with plasmon propagation through inhomogeneous media. We consider three dfferent geometries: an interface between two dfferent materials, a one dimensional perturbation, and a zero dimensional perturbation in an otherwise uniform electron system. We calculate scattering observables for plasmons in these geometries. For the interface geometry we also investigated the presence of plasmonic bound states localized near the interface, while for the second and third geometries we quantify the impact of non-local fects. Chapter 4 presents a theory of chiral plasmons in materials with a non-trivial Berry curvature in the electronic band structure. We firstly employ the results of Chapter 3 to obtain a semi-classical theory of Chiral Berry Plasmons (CBPs) at a generic interface between two materials having different Berry uxes across the Fermi surface. We then test the impact of different types of screened electron-electron interaction, and of a finite damping rate on the dispersion and lifetime of CBPs.