ABSTRACT
CONTENTS 2.1 Introduction ............................................................................................. 78 2.2 Theoretical Model and Computational Techniques .......................... 79 2.3 Polyacetylenes and Polydiacetylenes ................................................... 82
2.3.1 The Exciton-Basis VB Theory .................................................... 83 2.3.2 Justification of the SCI ................................................................ 86
2.4 Poly-paraphenylenes and Poly-paraphenylenevinylenes .................. 87 2.4.1 SCI and Parameterization of the PPP Hamiltonian ............... 87 2.4.2 Ultrafast Spectroscopy of PPV Derivatives ............................. 88
2.5 Semiconducting Single-Walled Carbon Nanotubes .......................... 91 2.5.1 Parameterization and Boundary Conditions .......................... 92 2.5.2 Nanotube Transverse Excitons ................................................. 94
2.5.2.1 One-Electron Limit ...................................................... 94 2.5.2.2 Nonzero Coulomb Interaction ................................... 96 2.5.2.3 Transverse Exciton and Its Binding Energy ............. 98 2.5.2.4 Splitting of the Allowed Transverse Optical
Absorption .................................................................... 99 2.5.3 Longitudinal Excitons in S-SWCNTs ..................................... 100
2.5.3.1 Dark Excitons and Electronic Structure with Many-Body Coulomb Interactions .......................... 100 2.5.3.2 Energy Manifolds....................................................... 101 2.5.3.3 Longitudinal Exciton Energies and Their
Binding Energies ........................................................ 102 2.5.4 Ultrafast Spectroscopy of S-SWCNTs .................................... 106
2.6 Conclusions and Future Work ............................................................ 108 Acknowledgments ..........................................................................................110 References .........................................................................................................110
Semiconducting carbon-based organic π-conjugated systems have been intensely investigated over the past several decades. In particular, their photophysics has been and continues to be of strong interest because of fundamental curiosity as well as current and promising technological applications. From a fundamental perspective, interest in carbon-based π-conjugated systems originates from their remarkable differences from the conventional inorganic band semiconductors. In contrast to the latter, strong, short-range, repulsive Coulomb interactions occur among the π-electrons in the organics, and these interactions contribute to a significant fraction of the optical gap. Theoretical understanding of π-conjugated systems therefore necessarily requires going beyond traditional band theory. Experimentally, even as exciton formation is found to be common in these materials, the standard technique of comparing the thresholds of linear absorption and photoconductivity for the determination of the exciton binding energy fails in noncrystalline organic materials because of the existence of disorder and inhomogeneity in these systems. Nonlinear optical spectroscopy and, in particular, ultrafast modulation spectroscopy have played valuable roles in elucidating the underlying electronic structures and photophysics of π-conjugated systems.
