Optical Properties of Carbon Conjugated Systems

Abstract

Conjugated carbon systems have played an important role historically in the theoretical study of physical phenomena and are finding many modern-day applications in electronic devices. Raman spectroscopy is a powerful tool in calibrating the structure of conjugated carbon systems and in studying their carrier dynamics, both of which are important to their potential applications. In Chapter 1 and 2, I provide a comprehensive understanding of the Raman spectrum of polyacetylene and graphene under the framework of the Kramers-Heisenberg-Dirac theory. Graphene is made up of $sp^2$-hybridized two-dimensional carbon lattice consisting of conjugated hexagonal cells. It shows extraordinary optical properties because of its low-dimensionality and unique electronic band structure. Graphene has found use in transparent electrodes, optical display materials and opto-electronics such as photodetectors, optical modulators, among many more. A proper understanding of the carrier dynamics in graphene is key to realizing its potential application in high-speed photonics and optoelectronics. In Chapter 3, we present a new paradigm for understanding optical absorption and hot electron dynamics experiments in graphene. In Chapter 4, we focus on the unique terahertz property of graphene, which has attracted a lot of recent attention due to its novel optoelectronic applications. We show that it is the coherence length of electrons that produces the peculiar terahertz properties in graphene. Single-wall carbon nanotubes (SWNTs) are nanometer-diameter cylinders consisting of a single graphene sheet wrapped up to form a tube. There has been a lot of recent activity exploring the electrical properties of SWNTs and their potential applications in electronics since their discovery in the early 1990s. In Chapter 5, I extend the methods used to understand polyacetylene and graphene Raman spectrum to explain various Raman spectrum features of SWNTs. Phonon-assisted light absorption in materials is an important optical process both from a fundamental and a technological point of view. Silicon is a commercially successful photovoltaic material because of the indirect optical transitions that enable photon capture in the spectral region between the indirect ($1.1~\text{eV}$) and direct ($3.4~\text{eV}$) band gaps. Despite its importance, only a very limited number of first-principles studies of phonon-assisted optical absorption spectra exist. In Chapter 6, we provide a new paradigm based on the Born-Oppenheimer approximation with light-matter interaction to calculate silicon's phonon-assisted absorption spectrum. %Carbon conjugated systems play an important role not only in the theoretical study of physical phenomena in the history of scientific development but also in modern applications in electronic devices. Raman spectrum is a powerful tool not only to calibrate structures of these materials, but also to study their carrier dynamics, both of which are key to their potential applications. In Chapter 1 and 2, we provide a comprehensive understanding of polyacetylene and graphene Raman spectrum under the framework of Kramers-Heisenberg-Dirac theory. %Graphene, with its $sp^2$-hybridized honeycomb two-dimensional carbon lattice consisting of conjugated hexagonal cells, shows extraordinary optical properties because of its dimensionality and unique electronic band structure. It has been applied in transparent electrodes, optical display materials and opto-electronics such as photodetectors, optical modulators, and so on. A proper understanding of the carrier dynamics in graphene is key to its potential applications in high-speed photonics and optoelectronics. In Chapter 3, we present a new paradigm for understanding optical absorption and hot electron dynamics experiments in graphene. The unique terahertz property of graphene attracts a lot of recent attentions due to its novel optoelectronic applications. In Chapter 4, we show that it is the coherence length of electrons that gives peculiar terahertz properties in graphene. %Single-Wall Carbon Nanotubes (SWNTs) are nanometer-diameter cylinders consisting of a single graphene sheet wrapped up to form a tube. There has been intense activity exploring the electrical properties of these systems and their potential applications in electronics since their discovery in the early 1990s. In Chapter 5, methods developed to understand polyacetylene and graphene Raman spectrum are applied to explain various Raman features of SWNTs. %The phonon-assisted light absorption in materials is an important optical process both from a fundamental and from a technological point of view. Silicon is a commercially successful photovoltaic material because of the indirect optical transitions that enable photon capture in the spectral region between the indirect (1.1 eV) and direct(3.4 eV) band gaps. Despite their importance, only a very limited number of first-principles studies of phonon-assisted optical absorption spectra exist. In Chapter 6, we provide a new paradigm based on Born-Oppenheimer approximation and light-matter interaction to calculate Silicon phonon-assisted absorption spectra.