The nature of the interaction of light with matter is a long-standing subject of great interest in condensed matter physics. Here I study the behavior of three electromagnetic effects arising from the coupling of light to two-dimensional electron systems: the Casimir effect, excitons in an insulator, and the formation of polaritons in a cavity.

I begin by examining how the Casimir effect is affected by material properties. First we consider using the Casimir force as a probe of a change in the topology of a material's Fermi surface called a Lifshitz transition. Specifically, I study a spin-orbit coupled semiconducting system, which can be made to undergo this sort of transition with an external magnetic field, and find that the signature of this transition is a non-analyticity in the Casimir force at the transition point.

I next consider how the phenomenon of weak localization can be used as a test of the role of disorder in the Casimir effect between metallic objects. I show how the sensitive dependence of the conductivity of a two-dimensional disordered metal on both temperature and magnetic field should translate into similar sensitivities of the Casimir force, assuming effects of disorder should be included at all.

Next, I examine excitons formed in the bulk of an insulator as a system transitions between topological and trivial insulating phases, finding that the phases have different signatures in the exciton spectrum. This can be understood as an effect of the Berry curvature of the model, giving an indirect glimpse of topological properties.

I construct a semiclassical model of the system to develop a qualitative intuition, then move to a numerical calculation in a full quantum model.

Finally, I consider the formation of polaritons inside of a photonic cavity containing a two-dimensional superconducting layer. I show how a coupling can be engineered between cavity photons resonant with a collective mode of the superconductor called the Bardasis-Schrieffer mode, leading to hybridized superconductor polariton states. Motivated by exciton polariton condensates, I conjecture that a phase-coherent density of these objects could produce an exotic $s\pm id$ superconducting state.