Light-matter interaction in two-dimensional transport

This Thesis considers some problems concerning light-matter interactions in the context of two-dimensional electron transport. In Chapter 1, we review some theoretical and experimental facts that are relevant for the results of the following Chapters, in particular, the hydrodynamic regime of electronic transport, the cavity engineering of materials, and the formalism of quantum field theory of many-body systems. In Chapter 2, we consider how the device geometry affects the Dyakonov–Shur mechanism of terahertz photodetection. Previous theoretical analyses of the mechanism always assume that the gate of the transistor, which is coupled to the antenna receiving the THz signal, is as long as the channel itself, at odds with typical experimental devices, where short gates are usually employed. We overcome this limitation and provide a complete theory of Dyakonov–Shur photodetection in the presence of short gates. In Chapter 3, we consider how the properties of a Fermi liquid can be modified by the coupling with a passive cavity. We explicitly show that the Fermi velocity of graphene is modified by a van der Waals polaritonic cavity formed by natural hyperbolic crystals and metal gates. In Chapter 4, we consider the possibility of controlling the superconductivity of a two-dimensional material with its dielectric environment. In particular, we consider the onset of superconductivity in twisted bilayer graphene, at twist angles larger than the magic angle, by resonant coupling between its plasmonic collective modes and optical phonons in a nearby polar dielectric.