A. Walsh

Screening of Excitons in Single, Suspended Carbon Nanotubes

Resonant Raman spectroscopy of single carbon nanotubes suspended across trenches displays red-shifts of up to 30 meV of the electronic transition energies as a function of the surrounding dielectric environment. We develop a simple scaling relationship between the exciton binding energy and the external dielectric function and thus quantify the effect of screening. Our results imply that the underlying particle interaction energies change by hundreds of meV.

Optical determination of electron-phonon coupling in carbon nanotubes

We report on an optical method to directly measure electron-phonon coupling in carbon nanotubes by correlating the first and second harmonic of the resonant Raman excitation profile. The method is applicable to 1D and 0D systems and is not limited to materials that exhibit photoluminescence. Experimental results for electron-phonon coupling with the radial breathing mode in 5 different nanotubes show coupling strengths from 3-11 meV. The results are in good agreement with the chirality and diameter dependence of the e-ph coupling calculated by Goupalov et al.

Exciton-mediated one-phonon resonant Raman scattering from one-dimensional systems

We use the Kramers-Heisenberg approach to derive a general expression for the resonant Raman scattering cross section from a one-dimensional (1D) system explicitly accounting for excitonic effects. The result should prove useful for analyzing the Raman resonance excitation profile line shapes for a variety of 1D systems including carbon nanotubes and semiconductor quantum wires. We apply this formalism to a simple 1D model system to illustrate the similarities and differences between the free electron and correlated electron-hole theories.

Electron correlation effects on the femtosecond dephasing dynamics of E22 excitons in (6,5) carbon nanotubes.

Highly nonlinear pump fluence dependence was observed in the ultrafast one-color pump-probe responses excited by 38 fs pulses resonant with the E(22) transition in a room-temperature solution of (6,5) carbon nanotubes. The differential probe transmission (ΔT/T) at the peak of the pump-probe response (τ = 20 fs) was measured for pump fluences from ∼10(13) to 10(17) photons/pulse cm(2). The onset of saturation is observed at ∼2 × 10(15) photons/pulse cm(2) (∼8 × 10(5) excitons/cm). At pump fluences >4 × 10(16) photons/pulse cm(2) (∼1.6 × 10(6) excitons/cm), ΔT/T decreases as the pump fluence increases. Analogous signal saturation behavior was observed for all measured probe delays. Despite the high exciton density at saturation, no change in the E(22) population decay rate was observed at short times (<300 fs). The pump probe signal was modeled by a third-order perturbation theory treatment that includes the effects of inhomogeneous broadening. The observed ΔT/T signal is well-fit by a pump-fluence-dependent dephasing rate linearly dependent on the number of excitons created by the pump pulse. Therefore, the observed nonlinear pump intensity dependence is attributed to the effects of quasi-elastic exciton-exciton interactions on the dephasing rates of single carbon nanotubes. The low fluence total dephasing time is 36 fs, corresponding to a homogeneous width of 36 meV (290 cm(-1)), and the derived E(22) inhomogeneous width is 68 meV (545 cm(-1)). These results are contrasted with photon-echo-derived parameters for the E(11) transition.

Scaling of exciton binding energy with external dielectric function in carbon nanotubes

Abstract We develop a scaling relationship between the exciton binding energy and the external dielectric function in carbon nanotubes. We show that the electron–electron and electron–hole interaction energies are strongly affected by screening yet largely counteract each other, resulting in much smaller changes in the optical transition energy. The model indicates that the relevant particle interaction energies are reduced by as much as 50% upon screening by water and that the unscreened electron–electron interaction energy is larger than the unscreened electron–hole interaction energy, in agreement with explanations of the “ratio problem.” We apply the model to measurements of the changes in the optical transition energies in single, suspended carbon nanotubes as the external dielectric environment is altered.

Spectroscopic properties unique to nano-emitters.

The spectral position of light emission from an individual carbon nanotube is shown to depend on the location of the nanotube within the focal spot, while no such effect is present for macroscopic emitters. In addition, in contrast to macroscopic emitters, the measured line width from the nanotube emitter is independent of spectrometer entrance slit width. The effects are general for any nanoscale optical emitter with at least one dimension smaller than the optical diffraction limit.

The Effect of Excitons on Raman Excitation Profiles in One-Dimensional Systems

We use the Kramers-Heisenberg approach to derive a general expression for the resonant Raman scattering cross section from a one-dimensional system explicitly accounting for excitonic effects

Nano-optics of carbon nanotubes: measurement of unperturbed optical transition energies

In this work we present resonant inelastic light scattering (Raman) studies of individual tubes suspended in air. Using high resolution micro-Raman spectroscopy with tunable filters for high throughput we have mapped the resonance Raman profiles for a series of individual SWNTs in the 2n+m = 22 and 29 families and found clear evidence of excitonic interactions from the Raman measurements. Individual suspended SWNTs are grown across etched trenches on a quartz substrate with the chemical vapor deposition technique. For a single suspended tube, the laser excitation energy is tuned to find the electronic resonance, indicated by an intensity maximum of the Raman radial breathing mode (RBM). The Stokes and anti-Stokes double-peaks are offset in energy as expected from incoming and outgoing light resonance with the electronic level. It is demonstrated that the double peaks in the resonance window are separated by the RBM phonon energy, determining the width of the resonance profile