Session H20: Focus Session: Carbon Nanotubes: Excitonic Effects

Fluorescence Correlation Spectroscopy of Single-wall Carbon Nanotubes

We demonstrate the application of fluorescence correlation spectroscopy (FCS) for the characterization of semiconductor type single-wall carbon nanotubes (SWCNT) in aqueous solution at low concentrations. The technique relies on the intrinsic nanotube bandgap luminescence in the near infrared (NIR) range and does not require nanotube functionalization. The nanotubes used in this study have been dispersed in solution of sodium deoxycholate and length fractionated via centrifugation in an iodixanol density gradient. The (6,5) type nanotubes were resonantly excited by focusing a circularly-polarized 568~nm laser beam into a diffraction limited spot in solution and the luminescence intensity fluctuations were detected at wavelengths above 950~nm using a custom FCS setup with enhanced NIR transmission optics. Correlation functions were analyzed using a model of segmental dynamics of weakly bending rods, modified to account for an additional fast relaxation mode associated with nanotube rotational dynamics and its polarization dependent luminescence. The accessible sample concentration range and the optimum excitation power range were identified. Sample luminescent signal stability significantly exceeding a typical measurement time of few minutes was demonstrated.   

Chirality-Dependent Electron-Hole Asymmetry in Single-Walled Carbon Nanotubes Probed by Direct Observation of Transverse Quasi-Dark Excitons

We studied the electron-hole (e-h) asymmetry between valence and conduction bands in single-walled carbon nanotubes (SWNTs) through the direct observation of spin-singlet transverse dark excitons using polarized photoluminescence excitation spectroscopy. The intrinsic e-h asymmetry lifts the degeneracy of the transverse exciton wavefunctions at two equivalent K and K' valleys in momentum space, which gives finite oscillator strength to transverse dark exciton states. Chirality-dependent spectral weight transfer to transverse dark states was clearly observed, indicating that the degree of the e-h asymmetry depends on the specific nanotube structure. Based on comparison between theoretical and experimental results, we evaluated the band asymmetry parameters in graphene and various carbon nanotube structures.   

Excitons and High-Order Optical Transitions in Individual Carbon Nanotubes

We address the issue of the excitonic nature of high-lying optical transitions in single-walled carbon nanotubes (SWNTs) by means of Rayleigh scattering spectroscopy of freely suspended individual nanotubes. A careful analysis of the E33 and E44 transitions in semiconducting and the M22 transitions in metallic nanotubes reveals that in both cases the lineshape is consistent with an excitonic model, but not with one involving free carriers. For semiconducting species, sidebands are observed at $\sim $200 meV above the main electronic transitions. These features are ascribed to exciton-phonon bound states. Such sidebands are barely visible for metallic nanotubes, as expected from the reduced strength of excitonic interactions in these systems. These findings [1] shed light on the nature of high-order optical transitions in SWNTS [2] and the strength of exciton-phonon coupling in metallic SWNTs [3,4]. \textbf{References:} [1] S. Berciaud \textit{et al.,} submitted (2009) [2] P.T. Araujo \textit{et al.}, PRL \textbf{98}, 067401 (2007) [3] H. Zeng et al., PRL \textbf{102}, 136406 (2009) [4] S. Berciaud \textit{et al.,} Nano Lett. \textbf{7} 1203 (2007)   

Magnetic Brightening of Dark Excitons in Carbon Nanotubes at Ultralow Temperatures

Although progress has been made in understanding the role of dark excitons in single-walled carbon nanotubes (SWNTs), current theory at low temperatures is still unconfirmed. In particular, at low temperatures where the thermal energy is less than the dark-bright splitting energy, all excitons should populate the lowest dark excitonic state and cause the disappearance of photoluminescence (PL). Here, we utilize a fiber-optic-equipped dilution refrigerator and superconducting magnet system to measure temperature dependent magnetic brightening of the PL of DNA-wrapped CoMoCAT SWNT thin films in a polyacrylic acid matrix. Measuring the magnetic field dependence to 5 T at 50 mK and 4.3 K with an excitation of 670 nm, we obtained an unexpected PL for 50 mK at zero-field comparable to zero-field PL at 4.3 K. Also, the magnitude of magnetic brightening does not change between 50 mK and 4.3 K. Such results are contrary to current theory, and we will discuss possible explanations such as a non-thermal distribution of excitons and defect-induced partial brightening of the dark state.   

Trench width dependence of photoluminescence intensity from individual suspended carbon nanotubes

As-grown, air-suspended carbon nanotubes (CNTs) offer the possibility to optically investigate the intrinsic properties of CNTs. We prepared trenches of various widths on SiO$_{2}$/Si substrates and suspended CNTs grown by chemical vapor deposition. Individual suspended CNTs were identified by taking photoluminescence (PL) images using a home-built laser-scanning confocal microscope system. PL excitation spectra were used to determine the chirality, and the orientation was measured by polarization spectroscopy. After such characterization, trench width dependence of the PL intensity was investigated. We observed that PL diminished as the trench width decreased, and extrapolation of the data yields quenching of PL at nonzero trench widths. By analyzing the data, it may be possible to obtain the diffusion length of excitons in pristine CNTs.   

Non-radiative Exciton Decay in Single-walled Carbon Nanotubes

Experiments have shown step-wise changes in the fluorescence intensity from single-walled carbon nanotubes [1,2]. It has been proposed that the underlying mechanism for the step-wise changes is diffusion-limited quenching of excitons at defects [1]. This property has been used to demonstrate single-molecule detection for biological applications [3]. We perform a Monte-Carlo simulation of nanotube fluorescence with a diffusion-limited quenching model. The fluorescence intensity is seen to depend on the mean-square distance between defects, implying a nonlinear dependence on the number of defects. The intensity for consecutive defect counts can overlap depending on the positions of the defects. \\[4pt] [1] Cognet, L. et al. Science 316, 1465-1468 (2007).\\[0pt] [2] Jin, H. et al. Nano Lett. 8, 4299-4304 (2008).\\[0pt] [3] Heller, D. A. et al. Nature Nanotech. 4, 114-120 (2009).   

Scanning tunneling microscopy and spectroscopy of single wall carbon nanotubes

Carbon nanotubes (CNTs) are fascinating candidates for fundamental studies of one dimensional materials as well as for future molecular electronics applications. Their electronic structure is directly linked to their chirality which controls their semiconducting of metallic character. The link between local electronic and atomic structure is a crucial parameter which can be investigated in detail by using Scanning tunnelling microscopy (STM) and spectroscopy (STS). STS measurements are dominated by a series of Van Hove singularities (VHS) which are usually successfully described by a tight-binding model. The energy position of these singularities and the related wavefunctions which can be seen as the molecular orbitals of CNTs are two fundamental characteristics of CNTs which will be discussed in details here. The experimental visualization of the wavefunctions associated to the VHS will be presented. They exhibit a symmetry breaking in semiconducting and metallic tubes which is well described by a tight-binding model. The energy position of the VHS will then be discussed in details. The recent experimental evidence of the major role of excitons in the optical transitions in CNTs has enlightened the importance of many-body effects in the electronic structure of CNTs. In STS experiments, the electronic gaps of semiconducting tubes supported by a metallic substrate are close to the optical transitions although STS is not sensitive to the excitons and should exhibit much larger VHS separation. We will discuss this issue and show the importance of many-body effects and tube-substrate interaction in the electronic bandgaps of semiconducting tubes.   

Exciton environment effect and exciton-phonon interaction of single wall carbon nanotubes

Optical transition energies of carbon nanotubes depend on metalicity and surrounding materials, which we call environmental effect. Using the extended tight binding exciton energy calculation combined with the screening effect of an exciton by surrounding materials, the transition energies are calculated as a function of diameter and dielectric constants and compared with the experimental results (P. T. Aroujo et al, PRL 103, 146802, (2009)). Now the all experimental data for a wide range of energy up to 3eV and for a wide range diameter up to 2nm can be fitted to the theoretical values in a high numerical accuracy within 60meV which is sufficient for assigning (n,m) values for many type of surfactant materials. We also report resonance Raman window values by a new, ETB exciton-phonon interaction, which will be compared with recent experimental measurement of radial breathing phonon Raman spectroscopy and excitation profile.   

High energy E$_{11}$ excitons above the continuum threshold in semiconducting single-walled carbon nanotubes

Although the excitonic nature of the primary photoexcitation has been firmly established in semiconducting single-walled carbon nanotubes (S-SWCNTs), the magnitude of the exciton binding energy is still being debated. Recent photoluminescence excitation experiments have detected excitons above the threshold of the continuum band predicted from two-photon absorption measurements in the (10,6) S-SWCNT \footnote{J. Lefebvre and P. Finnie, Nano Lett. \textbf{8}, 1890 (2008).} One interpretation of this experiment is that the exciton binding energy is much larger than previous estimates \footnote{J. Deslippe et al., Nano Lett. \textbf{9}, 1330 (2009).} We have performed configuration interaction calculations for the (10,6) S-SWCNT within the molecular PPP model that quantitatively reproduces the earlier estimate for the exciton binding energy and also finds excitons deep inside the continuum. A similar observation has previously been made for the conjugated polymer PPV.   

First-principles Calculations of the Quasiparticle and Optical Excitations in Metallic Carbon Nanostructures

The band structure of metallic single-walled carbon nanotubes (SWNTs) may be viewed as a cut of the graphene band structure through the Dirac point. Despite the screening due to carriers at the Fermi energy, metallic nanotubes have been predicted theoretically and confirmed experimentally to exhibit strong many-electron interaction effects in their quasiparticle and optical properties, including the existence of excitons. We have carried out a systematic study, based on the first-principles GW approach, of the quasiparticle properties of metallic nanotubes with diameters ranging from 0.5 to 1.5 nm as well as those of single-layer graphene sheets. We present results (converged with a very fine k-point grid) using both the generalized plasmon-pole (GPP) model as well as a direct treatment of dynamic screening from the RPA dielectric response. We calculate the quasiparticle band structures, lifetimes and spectral functions for both the doped and undoped cases. We present first-principles calculations of excitons and the optical response of metallic carbon nanotubes for the same range of diameters within the Bethe-Salpeter approach.   

Calculation of optical matrix elements in carbon nanotubes made simple

We have derived analytical expressions for dipole matrix elements describing interband optical transitions in carbon nanotubes for arbitrary light polarization and nanotube chiralities. We studied how the dependences of the optical matrix elements on the quantum numbers of the electronic states are affected by the time reversal symmetry.   

Optical Characterization of Double-walled Carbon Nanotube and Quantum Dot Heterostructures

We experimentally study the optical properties of double-wall carbon nanotube and quantum dot (QD) composites. The two materials are covalently linked by an aminoethanethiol ligand (AET), which, when in complex with the QD, gives a characteristic emission in the NIR originating from trap states. The magnitude of this NIR emission peak relative to the QD exciton peak is directly proportional to the quantity of linker in the solution. Studies of the AET ligand-exchanged QD alone show that it poorly passivates the surface of the QD, leading to a short and complex multiexponential exciton lifetime, characteristic of the existence of randomly distributed surface traps. In contrast, upon linking with the DWNT complex, the defect related emission disappears, leaving only exciton emission. More striking, the exciton emission recovers a nearly monoexponential behavior of $\sim $ 2.8 ns.   

Exciton Emission under Strong Exciton-Plasmon Coupling in Carbon Nanotubes

We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter ($\sim $1nm) semiconducting single-walled carbon nanotubes (CNs). We show that these interactions can result in strong exciton-interband-surface-plasmon coupling in individual CNs. This results in the exciton emission line (Rabi) splitting $\sim $0.1eV as the exciton energy is tuned to the nearest interband plasmon resonance of the CN [1]. The exciton-plasmon coupling strength we predict for individual CNs is close to that previously reported for hybrid plasmonic nanostructures artificially fabricated of organic semiconductors on metallic films [2]. The quantum confined Stark effect with an electrostatic field applied perpendicular to the CN axis can be used to control the exciton-plasmon coupling, and the exciton emission accordingly [3]. We expect this effect to open up paths to new tunable optoelectronic device applications of small-diameter semiconducting CNs.\\[4pt] [1] I.V.Bondarev, K.Tatur, L.M.Woods, Optics Commun. 282, 661 (2009). [2] J.Bellessa, et al., Phys. Rev. Lett. 93, 036404 (2004). [3] I.V.Bondarev, L.M.Woods, K.Tatur, Phys. Rev. B 80, 085407 (2009).