Phonon-assisted exciton relaxation dynamics for a (6,5)-enriched DNA-wrapped single-walled carbon nanotube sample

A series of nondegenerate pump-probe measurements were carried out on a DNA-wrapped single-walled carbon nanotube (SWNT) sample that is enriched with the (6,5) species. The pump pulse excites SWNTs at $\sim 1.567\mathrm{eV}$, which corresponds to an energy of two $D$-band phonons above the excitonic band edge of the (6,5) SWNT. The dynamics of different channels of exciton relaxation for the (6,5) SWNT is analyzed in terms of the decay in the time-resolved differential transmission spectra. By systematically varying the values of the probe energy, $E_{\text{probe}}$, to be in and out of resonance with the minority $(n,m)$ SWNT species in the sample at different pump fluence levels, an intermediate decay component associated with a hot phonon-absorption process is studied in detail. When the values of $E_{\text{probe}}$ were further tuned to off-resonance positions, photo-induced absorption processes could be investigated.

Figure 1

A transient spectrum monitoring the DT intensity vs delay time, for $E_{\text{probe}}\sim E_{11}^{1A-}(6,5)$ at $1.252\mathrm{eV}$, for a (6,5) enriched DNA-wrapped nanotube sample, pumped with $E_{\text{pump}}\sim 1.567\mathrm{eV}$ (pump fluence level fixed at $0.1\mathrm{J}∕{\mathrm{m}}^2$). The $\Delta T∕T_o$ data are plotted on a natural log scale. The inset shows a magnified portion of the plot to show the range of the delay time, pertinent to ${\tau }_{\mathrm{int}}$ more clearly.

Figure 2

(Color online) Fluence dependence of the different components in the relaxation dynamics for $E_{\text{probe}}\sim 1.252\mathrm{eV}$. The dotted lines are guides to the eyes. The faster components were measured with higher time resolution $\left(40\mathrm{fs}\right)$, over $20\mathrm{ps}$. To determine ${\tau }_{\text{slow}}$ more accurately, fluence-dependent experiments were carried out over $50\mathrm{ps}$ with lower time resolution $\left(120\mathrm{fs}\right)$ and higher pump fluence. Fluence dependence of (a) the two faster components corresponding to intraband processes and (b) the slower component corresponding to the dynamics of the interband recombination. (c) Shows that for the initial $20\mathrm{ps}$ of the decay process, the relative weight for the intermediate process increases with the pump fluence.

Figure 3

The schematic diagram and the respective DT spectra for five different probe energies. (a) A schematic diagram of different values of $E_{\text{probe}}$ relative to the band-edge energies of different nanotubes. The values of $E_{\text{probe}}$ from $O_1$ to $O_5$, respectively, are 1.158, 1.198, 1.222, 1.252, and $1.272\mathrm{eV}$. (b) DT spectra for different values of $E_{\text{probe}}$. Notice that DT changes sign as $E_{\text{probe}}$ moves in and out of resonance with the (6,5) and (7,5) nanotubes. We use the dotted lines as guides for the eyes to mark the zero DT line for the respective DT spectra. The positive DT intensities are normalized to aid with the line-shape comparison.

Figure 4

(a) A schematic diagram of relaxation from $a$ to the $1A-$ excitonic state $c$ by emitting two $D$-band phonons (see text). The black arrow denotes a fast phonon-emission process originating from an exciton-bound phonon state, whereas the gray arrow denotes a slow process originating from a real excitonic state. (b) A schematic diagram of a scenario in which the band-edge exciton population can be depleted via phonon absorption. The experiment was carried out for the case where $E_{\text{probe}}=E_{11}^{1A-}(6,5)$, corresponding to point $c$.

Figure 5

Schematic diagram of two possible scenarios for the photoinduced absorption process when $E_{\text{probe}}$ does not correspond to excitonic band-edge energies. (a) A band-edge exciton at $o$ is created by exciting an electron from ground state $z$ to virtual state $v$ and combining with an optical phonon. (b) A band-edge exciton at $o$ can combine with a photon and access a higher continuum mobile band state at $E_{ii}$, denoted by $h$.