Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 102-114).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Lead Halide Perovskites (LHPs) have emerged as an outstanding optical material, chiefly as attractive options for studies of light emission, due to their high quantum efficiencies, broad wavelength tuneability via chemical substitution, and facile growth conditions. LHPs have also been increasingly considered as an ideal candidate for exploring applications of exciton-polariton condensation, with a recent explosion of research in this area. The physical properties of LHPs are distinct from traditional materials often used to study exciton-polaritons, leading to debates over photo-physical mechanisms of stimulated emission, and interpretation of experimental results. This thesis addresses these debates in two parts, discussing (1) how the relatively low exciton-binding energy and phonon-bottleneck effects often leads to exciton dissociation prior to the laser powers needed to observe stimulated emission, and (2) how the optical birefringence associated with bulk CsPbBr3 at cryogenic temperatures will produce novel optical potentials which amount to a synthetic spin-orbit coupling of exciton-polaritons within a perovskite microcavity. These conclusions are reached by a combination of static and time-resolved spectroscopies, along with polarization-resolved Fourier-imaging optical techniques.

Density functional theory (DFT) provides an affordable computational tool to understand electronic structure of various molecules and solids. However, the use of DFT is still challenging to investigate nanomaterials of intermediate size that are too small to assume translational symmetry and too large to be considered as molecules. This thesis focuses on developing cost-effective but accurate computational methods for nanomaterials and using the methods to rationalize and predict experimental behaviors. A notable difference of a nanomaterial from its bulk counterpart is that its properties are exceptionally sensitive to the dielectric environment, requiring a proper treatment of the surrounding dielectrics for an accurate understanding. The consequences of heterogeneous dielectric screening on transition metal dichalcogenides are studied by developing a new theory based on classical electrostatics, which closely reproduced the band gaps and optical gaps calculated by the ab initio GW approximation and the Bethe-Salpeter equation (BSE). The relative insensitivity of the first optical transition energy observed by experiments was explained for the first time in terms of the cancellation effect of changes of the band gap and the exciton binding energy. The theory of heterogeneous dielectric environments is further developed to be used in an atomistic calculation of layered hybrid organic-inorganic lead halide perovskites via a tight-binding GW-BSE method. The binding energies of trions and biexcitons were also calculated using the stochastic variational method to give spectrum peak energies that show a good agreement with reported experimental measurements. Lastly, the tight-binding GW-BSE method is generalized into an atomistic, semiempirical approach to calculate the electronic structure and optical spectra of arbitrary nanomaterials, termed semiempirical GW (sGW) and BSE (sBSE).

Indiana University-Purdue University Indianapolis (IUPUI) / In this thesis, we focus on two broad categories of problems, exciton condensation and bound states, and two complimentary approaches, real and momentum space, to solve these problems. In chapter 2 we begin by developing the self-consistent mean field equations, in momentum space, used to calculate exciton condensation in semiconductor heterostructures/double quantum wells and graphene. In the double quantum well case, where we have one layer containing electrons and the other layer with holes separated by a distance $d$, we extend the analytical solution to the two dimensional hydrogen atom in order to provide a semi-quantitative measure of when a system of excitons can be considered dilute. Next we focus on the problem of electron-electron screening, using the random phase approximation, in double layer graphene. The literature contains calculations showing that when screening is not taken into account the temperature at which excitons in double layer graphene condense is approximately room temperature. Also in the literature is a calculation showing that under certain assumptions the transition temperature is approximately \unit{mK}. The essential result is that the condensate is exponentially suppressed by the number of electron species in the system. Our mean field calculations show that the condensate, is in fact, not exponentially suppressed. Next, in chapter 3, we show the use of momentum space to solve the Schr\"{o}dinger equation for a class of potentials that are not usually a part of a quantum mechanics courses. Our approach avoids the typical pitfalls that exist when one tries to discretize the real space Schr\"{o}dinger equation. This technique widens the number of problems that can presented in an introductory quantum mechanics course while at the same time, because of the ease of its implementation, provides a simple introduction to numerical techniques and programming in general to students. We have furthered this idea by creating a modular program that allows students to choose the potential they wish to solve for while abstracting away the details of how the solution is found. In chapter 4 we revisit the single exciton and exciton condensation in double layer graphene problems through the use of real space lattice models. In the first section, we once again develop the equations needed to solve the problem of exciton condensation in a double layer graphene system. In addition to this we show that by using this technique, we find that for a non-interacting system with a finite non-zero tunneling between the layers that the on-site exciton density is proportional to the tunneling amplitude. The second section returns to the single exciton problem. In agreement with our momentum space calculations, we find that as the layer separation distance is increased the bound state wave function broadens. Finally, an interesting consequence of the lattice model is explored briefly. We show that for a system containing an electron in a periodic potential, there exists a bound state for both an attractive as well as repulsive potential. The bound state for the repulsive potential has as its energy $-E_0$ where $E_0$ is the ground state energy of the attractive potential with the same strength.

A cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's. / Master of Science

We present a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments. Signals in both the probe and conjugate directions are discussed. The effects of recombination, non-radiative scattering and spatial and orientational diffusion are included. The analysis is applied to both a molecular and to a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. The theory is used to explain our recent observations in germanium. Included are discussions of picosecond transient grating self-diffraction measurements that can be understood in terms of an orientational grating produced by anisotropic (in k-space) state-filling. Though there have been predictions and indirect experimental evidence for isotropic state-filling in germanium, this is the first direct experimental indication of anisotropic state-filling in a semiconductor.

Electronic structure methods enable first-principles calculations of the properties of molecules and materials. But numerically exact calculations of systems relevant to chemistry are computationally intractable due to the exponentially scaling cost of solving the associated Schrödinger equation. This thesis describes the application of quantum Monte Carlo (QMC) methods that enable the accurate solution of this equation at reduced computational cost. Chapter 2 introduces the fast randomized iteration (FRI) framework for analyzing discrete-space QMC methods for ground-state electronic structure calculations. I analyze the relative advantages of applying different strategies within this framework in terms of statistical error and computational cost. Chapter 3 discusses the incorporation of strategies from related stochastic methods to achieve further reductions in statistical error. Chapter 4 presents a general framework for extending these FRI-based approaches to calculate energies of excited electronic states. Chapter 5 demonstrates that leveraging the best of these ground- and excited-state techniques within the FRI framework enables the calculation of very accurate electronic energies in large molecular systems. In contrast to Chapters 2–5, which describe discrete-space QMC methods, Chapter 6 describes a continuous-space approach, based on diffusion Monte Carlo, for calculating optical properties of materials with a particular layered structure. I apply this approach to calculate exciton, trion, and biexciton binding energies of hybrid organic-inorganic lead-halide perovskite materials using a semiempirical Hamiltonian.

In the past decade, research in the field of singlet fission, the process in which one high energy singlet fission exciton forms two lower energy triplet excitons, has seen a resurgence as a process that has the potential to improve solar energy conversion efficiency and contribute to a push for renewable energy. While an impressive motivation, there is still much progress in terms of understanding the physics of the process as well as improving molecular design for actual applications that needs to be made before this motivation can be fully realized. Two significant current hurdles in this field are the extraction of the newly formed triplet excitons from their entangled triplet pair state before recombination, and the lack of stable chromophores with viable energetics for singlet fission and high triplet energies for application purposes. Over the past five years, we have addressed these issues with targeted molecular design. Only a couple of studies have successfully separated the triplet pair state in intramolecular singlet fission systems. We create an intramolecular singlet fission system, a PDI-pentacene-pentacene-PDI tetramer, in which a charge transfer state is utilized to separate an electronically entangled triplet pair. We have also shown that singlet fission can be controlled as well as actually induced in chromophores by employing molecular contortion to tune the energetics. With this work, we have contributed to the motivation of using singlet fission in real-life applications.