Engineering surface plasmons and light-matter interactions in two-dimensional materials.

Abstract

Surface plasmons, the collective oscillations of electrons at the surface of a metal, have garnered significant attention due to the intensely confined electromagnetic fields they generate. The fields can be routed along the surface of the metal to be used as waveguides or can be used to strongly interact with and thus probe the properties of molecules. The discovery of graphene, and in general, two-dimensional materials, fueled a new generation of plasmonics, primarily driven by its tunable surface plasmon dispersion. Nonetheless, there are still multiple factors that limit further development and application of two-dimensional plasmonics. Most notably, significant losses in surface plasmons limit their propagation distance and coupling strength with molecules. Furthermore, robust control and routing of the surface plasmon is challenging. Finally, surface plasmons in two-dimensional materials are typically achiral and cannot distinguish between chiral molecules with different handedness. This thesis presents theoretical strategies to engineering surface plasmons in two-dimensional materials and the light-matter interactions they enable to overcome the limitations mentioned above. The approaches taken here span multiple length scales, from microscopic electronic band structure engineering to macroscopic spatial patterns imprinted on the conductivity of the two-dimensional material. We begin by giving a theoretical introduction to surface plasmons in two-dimensional materials. We then proceed by studying the surface plasmons in materials with a band structure hosting both electron and hole pockets. When an in-plane current is applied, we find that the electron distribution is shifted, enabling non-local single-particle relaxations that can transfer energy to the plasmon. When the plasmon dispersion overlaps with the phase space of these non-local transitions, we predict current-driven plasmon amplification and derive threshold currents that fall within present experimental reach. We then explore the engineering of the plasmon dispersion by imprinting spatially periodic conductivity landscapes, i.e., plasmonic crystals. We propose an approach to building plasmonic crystals by arranging metallic disks, which each support a ladder of multipolar localized plasmonic modes, into a periodic lattice. This approach is coined as a tight-binding plasmonic crystal. A plasmonic band structure emerges from the interaction between the localized plasmon modes. Most importantly, we find that the tight-binding plasmonic crystal has an intrinsic interaction that is analogous to the spin-orbit interaction in electronic systems. In a plasmonic Lieb lattice, we find that this interaction opens a topologically non-trivial band gap with spin-polarized helical edge states. In contrast, the interaction induces a spin-dependent splitting of the Dirac cones for a plasmonic honeycomb lattice, giving rise to symmetry-protected nodal lines. Lastly, we present results on light-matter interactions enabled by surface plasmons. The interaction between the localized surface plasmons of graphene nanoribbons and the vibrational modes of molecules is studied using classical theory. By extracting the complex coupled mode eigenvalues from the absorption spectrum of the system, we show that a non-Hermitian theory can be applied to understand the interaction. In particular, we identify the existence of an exceptional point and show that it can be easily accessed by tuning the Fermi energy of graphene and the incident angle of light. The sensitivity of the system to the molecular density is largely enhanced near the exceptional point. We also study the interaction between chiral surface plasmons and chiral molecules. Chiral surface plasmons are supported by twisted bilayer materials, which can be modeled using a chiral conductivity in addition to the usual electrical conductivity. We show that the chiral surface plasmons have a near-field optical chirality with a well-defined handedness. Furthermore, the interaction between the chiral surface plasmon and chiral molecules is found to be handedness-dependent and can therefore be used to determine the chirality of a given molecule. In the strong coupling limit, the splitting of the hybridized energy dispersion will depend on the relative handedness of the plasmon and molecule. We show that the strong field confinement of the chiral plasmon leads to a larger chiral discrimination factor when compared to approaches based on chiral cavities.