Many-Body Green’s Function Studies On The Spectra Of Carbon Nanotubes

Carbon nanotube (CNT), since its discovery during the synthesis of fullerene by Sumio Iijima in1991, has received great attention in the past decade in many fields, such as nanomedicines, field-effect transistors, and nanoscale sensors. Nanotubes can be categorized as single-walled nanotubes (SWCNTs) and multi-walled nanotubes (MWCNTs). Bare SWCNTs without encapsulation attract each. other and form crystalline "bundles"(or "ropes") through van der Waals interactions, i.e. pi-stacking. The chemical bonding of nanotubes is composed of sp2bonds, similar to those of graphite. Like other well-known forms of carbon, include diamond, graphite, lonsdaleite, fullerene and amorphous carbon, carbon nanotubes are also allotropes of carbon with a cylindrical nanostructure.The structure of the SWCNT can be conceptualized by wrapping a one-atom-thick graphene into a seamless cylinder. The way of wrapping graphene may be represented by a pair of indices (n, m), which is called chiral indices. The integers n and m denote the numbers of unit vectors along the two directions in the honeycomb crystal lattice of graphene. If m=0, the tubes are called zigzag nanotubes, while if n=m, the tubes are called armchair nanotubes. Otherwise, they are known as chiral nanotubes. According to the chiral indices, SWCNT can be divided into semiconducting nanotubes and metal nanotubes. Semiconducting nanotubes consist of types Ⅰ and Ⅱ SWNTs, depending on whether mod (2n+m)3=1or2, respectively, while metal nanotubes with mod(2n+m)3=0. The optical properties of SWCNTs also vary substantially with the tube diameters and chiral angles, so the measurement of the optical properties of individual SWCNTs has attracted a great interest. Combining spectrofluorimetric measurements with resonance Raman, Bachilo et al., have revealed distinct electronic absorption and emission transitions, and mapped these transitions to specific (n, m) SWCNTs. Thanks to the nonlinear density gradient ultracentrifugation, individual (n, m) species of SWCNTs can be highly enriched and the measurement of their optical properties become true. With all these developments, however, the PL efficiency of SWCNTs is still very low. Designing nanotube-based optical and electronic devices requires the controllable modification of the structures of carbon nanotubes to generate robust redshifted fluorescence.The physical mechanism of such redshifted excitons is still under debate. One common interpretation would be that they originate from the brightening (or activation) of intrinsic dark states, i.e., excitons that should be dipole forbidden due to the selection rule within a perfect SWCNT. For example, adsorbed hydrogen was thought to brighten the dark triplet excitons and thus reduce the PL quantum yield at E11. This assignment had been based on the comparison between the measured energies of these peaks and the calculated energies of dark excitons in some perfect SWCNTs via first-principles methods. However, this kind of assignment is debatable with respect to two important issues:(i) until now there has been no evidence that the oscillator strengths of the activated dark excitons are high enough to dominate the new PL peaks, and (ii) the Stokes shifts of the new PL peaks are much larger than those observed in perfect SWCNTs (about4meV).Here, in this dissertation, we use many-body Green’s function theory, as well as constrained density functional theory (CDFT), to study the spectrum of SWCNT. The significant and valuable conclusions obtained from this dissertation are listed as follows:1. The absorption spectra of semiconducting nanotubes. The band structure and optical absorption spectrum of a perfect (8,0) SWCNT can be calculated by GW+BSE. Two pronounced peaks (E11and E22) are found at1.53and1.79eV excitation energies, which are in good agreement with previous GW+BSE results and experiments (1.60and1.88eV for E11and E22, respectively). The exciton binding energies are about1eV,1order of magnitude larger than those in bulk semiconductors with similar band gaps. This strong excitonic effect arises from the onedimensional nature of the (8,0) SWCNT. The E11exciton is composed from band-to-band transitions between the HOMO band and the LUMO+3band, not between the HOMO band and the LUMO band, which can be attributed to the curvature.2. The optical spectra of oxygen atom doped nanotubes. We have investigated the absorption and emission spectra for oxygen doped (8,0) SWCNTs We have demonstrated that the perturbation of the doped oxygen atom to the electronic structure of the SWCNTs is little as the doping concentration is very low. So the broadening of absorption peaks can only be observed, instead of two peaks. The intense red-shifted emission peaks are ascribed to relaxation of the excitation state, where the strong Stokes shifts lead to redshifted PL peaks and dominate the spectrum. 3. The optical spectra of hydrogen atom doped nanotubes. Here, we have investigated the absorption and emission spectra for hydrogen doped (8,0) SWCNTs. The calculated results reveal that defect-induced impurity states appear upon hydrogen doping, and the optical selection rules change. Besides, the strong Stokes shifts also play an important role in the redshifted PL peaks.4. The optical spectra of nanotubes with defects. We have investigated the absorption and emission spectra for (8,0) SWCNTs with single vacancies (SVs) and Stone-Wales (SW) defects. We find that the SV and SW defects still exhibit a semiconducting band structure. Some localized electron states exist near the conduction band minimum and the valence band maximum. In both cases, the optical spectrum starts with spatially localized excitations below the E11transition. We believe that the oscillator strengths of activated optically dark excitons states are quite small and the new redshirted peaks may equally well result from new electronic states of the damaged SWCNTs. So, the defect-induced states may be responsible for the new PL peaks found experimentally. This holds in particular for the SW defect, which leads to excited states that is consistent with the experimental observation.5. Excited-state force for BSE. Many-body green’s function theory is the most effective first principles method to study the excited state properties. It has been made great success in the crystal, clusters and biological molecules in excited state investigation, but the methods and programs are still in the stage of development, compared with density functional theory. So far, to calculate the excited state forces, there are mainly two kinds of method:1combining perturbation theory and density functional perturbation theory to solve the excited state forces,2using the finite difference method to calculate the excited state forces. In this paper, we begin with the Bethe-salpter equation, and derive the analytical form of excited state forces.