Optical transition energies are widely used for providing experimental insight into the electronic band structure of single-wall carbon nanotubes (SWCNTs). While the first and second optical transitions in semiconducting carbon nanotubes have already been heavily studied, due to experimental difficulties in accessing the relevant excitation energy region, little is known about higher lying transitions. Here, I present measurements of the third and fourth optical transitions of small-diameter (0.7-1.2 nm), semiconducting single-wall carbon nanotubes via resonant Raman spectroscopy in the visible deep blue region (415-465 nm) and photoluminescence excitation spectroscopy in the ultraviolet and visible blue optical regions (280-488 nm). Diameter-dependent Raman radial breathing mode features, as well as resonant energy excitation maxima determined by Raman and photoluminescence measurements, are assigned to specific (n,m) nanotube species. The Raman intensity within a given 2n+m branch is found to increase with decreasing chiral angle, consistent with similar measurements for lower order optical states. Additionally, increased excitation line widths and weaker Raman intensities are observed as higher lying transitions are accessed for a given nanotube, in agreement with previous Raman measurements. Chiefly, a scaling law analysis that removes the chiral-angle-dependent contribution to the optical transition energy indicates that the third and fourth transition energies exhibit a significant deviation from the energy trend line observed for the first and second optical transitions, when the transition energies are plotted as a function of nanotube diameter. This deviation can be understood in the context of a change in the competition between exchange and excitonic correction terms. Furthermore, for semiconducting SWCNTs with diameters less than 0.9 nm, an additional deviation is observed that is interpreted as the first observation of crossing-over of the third and fourth transition energy trend lines for a given 2n+m branch and a chirality dependence in the many-body excitonic effects that becomes significant at high nanotube curvatures.

The armchair variety of single-wall carbon nanotubes (SWCNTs) is the only nanotube species that behaves as a metal with no electronic band gap and massless carriers, making them ideally suited to probe fundamental questions of many-body physics of one-dimensional conductors as well as to serve in applications such as high-current power transmission cables. However, current methods of nanotube synthesis produce bulk material comprising of a mixture of nanotube lengths, diameters, wrapping angles, and electronic types due to the inability to control the growth process at the nanometer level. As a result, measurements of as-grown SWCNTs produce a superposition of electrical and optical responses from multiple SWCNT species. This thesis demonstrates production of aqueous suspensions composed almost entirely of armchair SWCNTs using a post-synthesis separation method employing density gradient ultracentrifugation (DGU) to separate different SWCNT types based on their mass density and surfactant-specific interactions. Resonant Raman spectroscopy determines the relative abundances of each nanotube species, before and after DGU, by measuring the integrated intensity of the radial breathing mode, the diameter-dependent radial vibration of the SWCNT perpendicular to its main axis, and quantifies the degree of enrichment of bulk nanotube samples to exclusively armchair tubes. Raman spectroscopy of armchair-enriched samples of the G-band mode, which is composed of longitudinal (G-) and circumferential (G+) vibrations oscillating parallel and perpendicular to the tube axis, shows that the G- peak, long-held to be an indicator for the presence of metallic SWCNTs, appears only when electronic resonance with narrow-gap semiconducting SWCNTs occurs and shows only the G+ component in spectra containing only armchair species. Finally, by combining optical absorption measurements with nanotube composition as determined earlier via Raman scattering, peak fitting of absorption spectra indicates that interband transitions of armchair SWCNTs are strongly excitonic as shown by the highly symmetric peak lineshapes, a property normally attributed to semiconductors. Such lineshapes allow classification of armchair SWCNTs as a unique hybrid class of optical nanomaterial. Combining absorption and Raman scattering measurements establishes a distinct optical signature that describes the fundamental optical processes within armchair SWCNTs and lays the foundation for future studies of many-body photophysics and electrical applications.

The thesis presents experimental studies of device characteristics and vibrational properties of atomic layer thin graphene and molybdenum disulphide (MoS2). We carried out Raman spectroscopic studies on field effect transistors (FET) fabricated from these materials to investigate the phonons renormalized by carrier doping thus giving quantitative information on electron-phonon coupling. Below, we furnish a synoptic presentation of our work on these systems. Chapter1: Introduction Chapter1, presents a detailed introduction of the systems studied in this the¬sis, namely single layer graphene (SLG), bilayer graphene (BLG) and single layer molybdenum disulphide (MoS2). We have mainly discussed their electronic and vibrational properties in the light of Raman spectroscopy. A review of the Raman studies on graphene layers is presented. Chapter2: Methodology and Experimental Techniques Chapter 2 starts with a description of Raman instrumentation. The steps for isolating graphene and MoS 2 flakes and the subsequent device fabrication procedures involving lithography are discussed in detail. A brief account of the top gated field effect transistor (FET) using solid polymer electrolyte is presented. Chapter3: Band gap opening in bilayer graphene and formation of p-n junction in top gated graphene transistors: Transport and Raman studies In Chapter3 the bilayer graphene (BLG) field effect transistor is fabricated in a dual gate configuration which enables us to control the energy band gap and the Fermi level independently. The gap in bilayer energy spectrum is observed through different values of the resistance maximum in the back gate sweep curves, each taken at a fixed top gate voltage. The gate capacitance of the polymer electrolyte is estimated from the experimental data to be 1.5μF/cm2 . The energy gap opened between the valence and conduction bands using this dual-gated geometry is es¬timated invoking a simple model which takes into account the screening of gate induced charges between the two layers. The presence of the controlled gap in the energy band structure along with the p-n junction creates a new possibility for the bilayer to be used as possible source of terahertz source. The formation of p-n junction along a bilayer graphene (BLG) channel is achieved in a electrolytically top gated BLG FET, where the drain-source voltage VDS across the channel is continuously varied at a fixed top gate voltage VT(VT>0). Three cases may arise as VDS is varied keeping VT fixed: (i) for VT-VDS0, the entire channel is doped with electron, (ii) for VT-VDS= 0, the drain end becomes depleted of carriers and kink in the IDS vs VDS curve appears, (iii) for VT-VDS « 0, carrier reversal takes place at the drain end, accumulation of holes starts taking place at the drain end while the source side is still doped with electrton. The verification of the spatial variation of carrier concentration in a similar top gated single layer graphene (SLG) FET device is done using spatially resolved Ra¬man spectroscopy. The signature 2D Raman band in a single layer graphene shows opposite trend when doped: 2D peak position decreases for electron doping while it increases for hole doping. On the other hand, the G mode response being symmetric in doping can act as a read-out for the carrier concentration. We monitor the peak position of the G and the 2D bands at different locations along the SLG FET channel. For a fixed top gate voltage V T , both G and the 2D band frequencies vary along the channel. For a positive VTsuch that VT-VDS= 0, the peak frequencies ωGand ω2DωG/2D occur at the undoped frequency (ωG/2D)n=0 near the drain end while the source end corresponds to non-zero concentration. When VT-VDS<0, Raman spectra from hole doped regions (drain end) in the channels show an blue-shift in ω2Dwhile from the electron doped regions (near source) ω2Dis softened. Chapter4: Mixing Of Mode Symmetries In Top Gated Bilayer And Multilayer Graphene Field Effect Devices In Chapter4, the effect of gating on a bilayer graphene is captured by using Raman spectroscopy which shows a mixing of different optical modes belonging to differ¬ent symmetries. The zone-center G phonon mode splits into a low frequency (Glow) and a high frequency (Ghigh) mode and the two modes show different dependence on doping. The two G bands show different trends with doping, implying different electron-phonon coupling. The frequency separation between the two sub-bands in¬creases with increased doping. The mode with higher frequency, termed as Ghigh, shows stiffening as we increase the doping whereas the other mode, Glow, shows softening for low electron doping and then hardening at higher doping. The mode splitting is explained in terms of mixing of zone-center in-plane optical phonons rep¬resenting in-phase and out-of-phase inter-layer atomic motions. The experimental results are combined with the theoretical predictions made using density functional theory by Gava et al.[PRB 80, 155422 (2009)]. Similar G band splitting is observed in the Raman spectra from multilayer graphene showing influence of stacking on the symmetry properties. Chapter5: Anomalous dispersion of D and 2D modes in graphene and doping dependence of 2D ′and 2D+G bands Chapter 5 consists of two parts: Part A titled “Doping dependent anomalous dispersion of D and 2D modes in graphene” describes the tunability of electron-phonon coupling (EPC) associated with the highest optical phonon branch (K-A) around the zone corner K using a top gated single layer graphene field effect transistor. Raman D and 2D modes originate from this branch and are dispersive with laser excitation energy. Since the EPC is proportional to the slope of the phonon branch, doping dependence of the D and 2D modes is carried out for different laser energies. The dispersion of the D mode decreases for both the electron and the hole doping, in agreement with the recent theory of Attaccalite et. al [Nano Letters, 10, 1172 (2010)]. In order to observe D-band in the SLG samples, low energy argon ion bombardment was carried out. The D peak positions for variable carrier concentration using top-gated FET geometry are determined for three laser energies, 1.96 eV, 2.41 eV and 2.54 eV. However, the dispersion of the 2D band as a function of doping shows an opposite trend. This most curious result is quantitatively explained us¬ing a fifth order process rather than the usual fourth order double resonant process usually considered for both the D and 2D modes. Part B titled “Raman spectral features of second order 2D’ and 2D+G modes in doped graphene transistor” deals with doping dependence of 2D’ and 2D+G bands in single layer graphene transistor. The phonon frequency blue shifts for the hole doping and whereas it red shifts for electron doping, similar to the behaviour of the 2D band. The linewidth of the 2D+G combination mode too follows the 2D trend increasing with doping while that of 2D’ mode remains invariant. Chapter6: New Raman modes in graphene layers using 2eV light Unique resonant Raman modes are identified at 1530 cm−1 and 1445 cm−1 in single, bi, tri and few layers graphene samples using 1.96 eV (633 nm) laser excitation energy (EL). These modes are absent in Raman spectra using 2.41 eV excitation energy. In addition, the defect-induced D band which is observed only from the edges of a pristine graphene sample, is observed from the entire sample region using E L = 1.96 eV. Raman images with peak frequencies centered at 1530 cm−1, 1445 cm−1 and D band are recorded to show their correlations. With 1.96 eV, we also observe a very clear splitting of the D mode with a separation of ∼32 cm−1, recently predicted in the context of armchair graphene nanoribbons due to trigonal warping effect for phonon dispersion. All these findings suggest a resonance condition at ∼2eVdue to homo-lumo gap of a defect in graphene energy band structure. Chapter7: Single and few layer MoS2: Resonant Raman and Phonon Renormalization Chapter 7 is divided into two parts. In Part A “Layer dependent Resonant Raman scattering of a few layer MoS2”, we discuss resonant Raman scattering from single, bi, four and seven layers MoS2. As bulk crystal of MoS2is thinned down to a few atomic layers, the indirect gap widens turning into a direct gap semiconductor with a band gap of 1.96 eV in its monolayer form. We perform Raman study from MoS 2 layers employing 1.96 eV laser excitation in order to achieve resonance condition. The prominent Raman modes for MoS 2 include first order E12g mode at ∼383 cm−1 and the A1gmode at ∼408 cm−1 which are observed under both non resonant and resonant conditions. A1gphonon involves the sulphur atomic vibration in opposite direction along the c axis (perpendicular to the basal plane) whereas for E12g mode, displacement of Mo and sulphur atoms are in the basal plane. With decreasing layer thickness, these two modes shifts in opposite direction, the E12g mode shows a blue shift of ∼2cm−1 while the A1gis red shifted by ∼4cm−1 . Under resonant condi¬tion, apart from E12g and A1gmodes, several new Raman spectral features, which are completely absent in bulk, are observed in single, bi and few layer spectra pointing out the importance of Raman characterization. New Raman mode attributed to the longitudinal acoustic mode belonging to the phonon branch at M along the Γ-M direction of the Brillouin zone is seen at ∼230 cm−1 for bi, four and seven layers. The most intense region of the spectrum around 460 cm−1 is characterized by layer dependent frequencies and spectral intensities with the band near 460 cm−1 becoming asymmetric as the sample thickness is increased. In the high frequency region between 510-630 cm−1, new bands are seen for bi, four and seven layers. In Part B titled “Symmetry-dependent phonon renormalization in monolayer MoS2transistor”, we show that in monolayer MoS2the two Raman-active phonons, A1g and E21 g, behave very differently as a function of doping induced by the top gate voltage in FET geometry. The FET achieves an on-off ratio of ∼ 105 for electron doping. We show that while E12g phonon is essentially unaffected, the A1gphonon is strongly influenced by the level of doping. We quantitatively understand our experimental results through the use of first-principles calculations to determine frequencies and electron-phonon coupling for both the phonons as a function of carrier concentration. We present symmetry arguments to explain why only A1g mode is renormalized significantly by doping. Our results bring out a quantitative under¬standing of electron-phonon interaction in single layer MoS2.