Temperature dependence of photoluminescence spectra in hole-doped single-walled carbon nanotubes: Implications of trion localization

We studied the dimensionality of excitons and trions (charged excitons) in hole-doped single-walled carbon nanotubes (SWNTs) by means of photoluminescence (PL) spectroscopy. We found that the temperature ($T$) dependence of the PL intensity of the trions and excitons is significantly different, reflecting their dimensionality. The PL intensity of the trions was almost unchanged for 5–300 K, whereas clear $T^{-1/2}$ dependence of the exciton PL intensity was observed, which reflects the characteristic radiative decay rate of one-dimensional excitons. The results suggest that the radiative decay rate of the trions is independent of the temperature, which is the manifestation of the localization of the trions in hole-doped SWNTs.

Figure 1

Normalized PL spectra of hole-doped (orange line) and undoped (gray line) SWNTs measured at 280 K. The exciton and trion peaks are denoted by $X$ and $X^{+}$, respectively. The accumulation time of the PL spectra is 1 s for undoped and 10 s for hole-doped SWNTs, respectively.

Figure 2

(a) PL spectra of hole-doped SWNTs measured at various temperatures from 5 to 300 K. Inset shows the PL spectra of undoped SWNTs from 5 to 300 K. (b) PL spectra of trions ($X^{+}$) measured at 5, 140, and 300 K on an expanded energy scale. The solid line corresponds to the spectral fitting results for 300 K using Voigt functions. The decomposed PL peaks of (7,5) trions ($X^{+}$) and (7,6) excitons ($X$) are shown as black solid and dotted lines, respectively.

Figure 3

(a) Temperature dependence of the integrated PL intensity of excitons ($X$) in undoped SWNTs (red diamonds). The solid line corresponds to the calculated temperature dependence of the PL intensity assuming a 1D radiative decay rate and an exciton population derived from the three-level model. (b) Schematics of the four-level model consisting of trion ($X^{+}$), excitons ($X$) [bright (B) and dark (D) state], and ground states (Gr). The region surrounded by the dashed line corresponds to the schematic of the three-level model. The bright $|\mathrm{B}\rangle$ and dark $|\mathrm{D}\rangle$ states are the fine structures of the exciton level. The energy level of trions $|X^{+}\rangle$ is below the exciton levels ($|\mathrm{B}\rangle$ and $|\mathrm{D}\rangle$). (c) Normalized PL intensity of the trions ($X^{+}$) (blue squares) and excitons ($X$) (red circles) in hole-doped SWNTs as a function of temperature. The black line shows $T^{-1/2}$ independence, reflecting the 1D radiative decay rate, and the pink line shows constant behavior, reflecting the temperature-independent 0D radiative decay rate.