Microscopic theories of excitons and their dynamics

This thesis describes the development and application of microscopically-defined theories of excitons in a wide range of semiconducting materials. In Part I, I consider the topic of singlet exciton fission, an organic photophysical process which generates two spin-triplet excitons from one photoexcited spin-singlet exciton. I construct a theoretical framework that couples a realistic treatment of the static electronic structure with finite-temperature quantum relaxation techniques. This framework is applied separately, but consistently, to the problems of singlet fission in pentacene dimers, crystalline pentacene, and crystalline hexacene. Through this program, I am able to rationalize observed behaviors and make non-trivial predictions, some of which have been confirmed by experiment. In Part II, I present theoretical developments on the properties of neutral excitons and charged excitons (trions) in atomically thin transition metal dichalcogenides. This work includes an examination of material trends in exciton binding energies via an effective mass approach. I also present an experimental and theoretical collaboration, which links the unconventional disposition of excitons in the Rydberg series to the peculiar screening properties of atomically thin materials. The light-matter coupling in these materials is examined within low-energy models and is shown to give rise to bright and dark exciton states, which can be qualitatively labeled in analogy with the hydrogen series. In Part III, I explore theories of relaxation dynamics in condensed phase environments, with a focus on methodology development. This work is aimed towards biological processes, including resonant energy transfer in chromophore complexes and electron transfer in donor-bridge-acceptor systems. Specifically, I present a collaborative development of a numerically efficient but highly accurate hybrid approach to reduced dynamics, which exploits a partitioning of environmental degrees of freedom into those that evolve "fast" and "slow," as compared to the internal system dynamics. This method is tested and applied to the spin-boson model, a two-site Frenkel exciton model, and the seven-site Fenna-Matthews-Olson complex. I conclude with a collaborative analysis of a recently developed polaron-transformed quantum master equation, which is shown to accurately interpolate between the well-known Redfield and Forster theories, even in challenging donor-bridge-acceptor arrangements.