Topological nanophotonics combines the high sensitivity of nanophotonic systems with the robustness of topological states, presenting an exciting new platform for both nanotechnological applications and fundamental research in topological light-matter interactions. The work I present in this thesis focuses on topological insulator (TI) nanostructures and their interactions with light, with particular focus on the terahertz (THz) regime.
TIs are insulating in their bulk and host symmetry-protected, conducting surface states which are robust against disorder. These surface states manifest as a Dirac cone traversing the bulk band gap. TI nanostructures (all dimensions < 100 nm) exhibit a discretised Dirac cone due to quantum confinement of the topological surface states, with energy levels separated by THz frequencies. Due to their analogy with semiconductor quantum dots and
2D topological insulator quantum dots, I refer to this system as a topological quantum dot (TQD). The results of this thesis are organised thematically into three areas:
(i) I expand the current knowledge of TI nanostructure electronic structures, describing the surface states and energy levels for geometries ranging from the infinite
nanowire to a flat nanodisk within a single mathematical framework.
(ii) I investigate the coupling of TQD states with THz frequency light, including selection rules and the suppression of transitions away from the Dirac point when the TQD is placed in a high quality cavity, allowing for a closed system of energy levels. Using Monte Carlo simulations I demonstrate that a single TQD in a cavity will lase in the THz, with an ultra-low threshold. The creation of robust, low threshold lasers in the THz regime is a crucial frontier in modern applied physics, due to the notorious absence of practical technologies for generating and sensing radiation in the THz gap (0.1-10 THz). I show that thermal photons are abundant enough to pump the system, and present a road map to room-temperature THz lasing with no additional external pumping source.
(iii) I describe how the quantised TI surface states modify the bulk properties of the nanostructure via a new polariton mode (the SToP mode) [5], and present the
first experimental evidence of the SToP mode. I demonstrate how the SToP mode can be used to manipulate the THz behaviour of light in the environment
surrounding a TI nanostructure, by increasing the photonic local density of states by many orders of magnitude. This phenomenon has potential applications in nanotechnology and also presents a new way of probing topological properties of matter using light.
I hope that this thesis serves as a guide to students new to the wonderful and interdisciplinary topic of topological nanophotonics, and that my work contributes to a slightly better understanding of topological light-matter interactions at the nanoscale, and the manipulation of THz frequency light.