Exciton dynamics in single-walled nanotubes: Transient photoinduced dichroism and polarized emission

Ultrafast relaxation of photoexcitations in semiconducting single-walled carbon nanotubes ($S$-NTs) were investigated using polarized pump-probe photomodulation (with 150 fs time resolution) and cw polarized photoluminescence (PL). Both annealed and unannealed thin NT films and ${\mathrm{D}}_2\mathrm{O}$ solutions of isolated NTs were investigated. Various transient photoinduced bleaching (PB) and photoinduced absorption (PA) bands, which show photoinduced dichroism, were observed in the ultrafast photomodulation spectra of all NT forms. The PA and PB decay dynamics as a function of time, $t$, follow a power law, ${\left(t\right)}^{-\alpha }$ with $\alpha$ in the range of 0.7 to 1. Whereas the PA bands in $S$-NTs in solution uniformly decay, the PB bands, in contrast, have different decay dynamics across the spectrum, which originates from an ultrafast spectral shift. Nevertheless the dynamics of the PA and PB bands for NTs in solution are the same when the spectral shift is accounted for, indicating a common origin. In addition $S$-NTs in ${\mathrm{D}}_2\mathrm{O}$ solution show polarized PL emission bands in the mid infrared spectral range that follow almost exactly the infrared absorption peaks of the isolated NTs, as well as their transient PB spectrum. The PL emission shows a degree of polarization that agrees with that of the transient photoinduced dichroism. We therefore conclude that the primary photoexcitations in $S$-NTs are not free carriers, rather they are excitons that are confined along the nanotubes. We found that the transient relaxation kinetics of the excitons depend on the NT form. The fastest exciton dynamics (with sub-picosecond lifetime) characterizes the annealed film, whereas the slowest dynamics (with lifetime of tens of ps) characterizes the isolated NTs in ${\mathrm{D}}_2\mathrm{O}$ solution. From the polarization memory decay we could estimate the diffusion constant, $D$, and the diffusion length, $L_D$, of the excitons along the nanotube. For the annealed films at room temperature we found $D\approx 100{\mathrm{cm}}^2{\mathrm{s}}^{-1}$ and $L_D\approx 100\mathrm{nm}$. From the average PL polarization degree, which remains constant across the PL spectrum, and the transient polarization memory decay, we estimate the PL lifetime in NT solution to be of the order of 500 ps. This relatively long PL lifetime is dominated by nonradiative decay processes, which when coupled with the minute PL emission quantum efficiency indicates a very small radiative recombination rate. The weak radiative transition strength is consistent with recent excited state calculations that include electron-hole interaction, which predict that excitons in NTs are basically dark.

Figure 1

Absorption spectra $\alpha \left(\omega \right)$ of SWCNTs in different forms. (a) Annealed (solid line) and unannealed (dashed line) NTs films, and (b) NTs in ${\mathrm{D}}_2\mathrm{O}$ solution. The bands $A$, $B$ and $D$ are due to $S$-NT transitions; band $C$ is due to $M$-NT transition. Black lines with arrow down (up) show pump (probe) photon energies used in this work.

Figure 2

Transient PM spectra measured at $t=0$ of annealed SWCNT film (a) and NTs in ${\mathrm{D}}_2\mathrm{O}$ solution (b). Various PA and PB bands are assigned.

Figure 3

Comparison between absorption $\alpha \left(\omega \right)$, PL emission, and transient PB spectra at $t=0$, for NTs in ${\mathrm{D}}_2\mathrm{O}$ solution.

Figure 4

(Color online) Transient polarized PB response at 0.67 eV for SWCNTs of different forms; both $\mathrm{\Delta }{T}_{\Vert }$ and $\mathrm{\Delta }{T}_{\perp }$ components are shown. (a) Annealed film excited with two different pump photon energies (see inset) and (b) unannealed film.

Figure 5

(Color online) Transient polarized PM response of NTs in ${\mathrm{D}}_2\mathrm{O}$ solution excited at 1.6 eV and probed at various photon energies within the PB bands (a) and PA bands (b).

Figure 6

(Color online) (a) Transient PB spectra of NTs in ${\mathrm{D}}_2\mathrm{O}$ solution at three different times between the pump and probe pulses; the inset shows the peak position of the PB band at $\approx 0.85\mathrm{eV}$ at various times up to 40 ps. (b) The calculated transient decay of the PB band at various probe photon energies using the model described in the text.

Figure 7

(Color online) Transient polarized PM response of NTs in ${\mathrm{D}}_2\mathrm{O}$ solution at various probes photon energies, where both $\mathrm{\Delta }{T}_{\Vert }$ and $\mathrm{\Delta }{T}_{\perp }$ components are shown (a) for the PA band and (b) for the PB band.

Figure 8

(Color online) The polarization memory dynamics in SWCNTs of various forms. (a) Annealed (at two pump photon energies) and unannealed films at 0.675 eV (PB) and (b) NTs in solution at two different probe photon energies, at 0.96 (PB) and 0.70 eV (PA), respectively. Fitting lines through the data points for the polarization memory decay are also shown.

Figure 9

(Color online) The parallel and perpendicular components (with respect to the pump polarization) of the polarized PL emission spectrum of NTs in solution. The spectrum of the PL polarization degree, $P_{\mathrm{PL}}$ (see text) is also shown.

Figure 10

Schematic representation of the time-dependent pump and probe polarizations, excitons diffusion and polarization, and the geometrical relationship between the three.