Exciton energy transfer between the inner and outer tubes in double-walled carbon nanotubes

We have studied photoluminescence (PL) spectrum and dynamics of the inner nanotubes in double-walled carbon nanotubes (DWNTs) and compared PL properties between DWNTs and single-walled carbon nanotubes (SWNTs). The PL peak energies of the inner tubes are redshifted from those of SWNTs with the same chiral indices. This PL redshift is enhanced with an increase in the inner tube diameter. The PL lifetime of DWNTs increases with a decrease in the inner tube diameter. The diameter dependence of PL dynamics is explained by exciton energy transfer between the inner and outer tubes through Förster-type dipole-dipole interaction.

Figure 1

(Color online) PL excitation maps of (a) SWNTs and (b) DWNTs. The assigned chiral indices are indicated in the figures.

Figure 2

(Color online) PL spectra of SWNTs and DWNTs under excitation at (a) 1.70 and (b) 1.96 eV. (c) Diameter dependence of the PL peak shift of DWNTs from the SWNTs with the same chiral indices.

Figure 3

(Color online) Normalized fast decay of the FEC signals of the DWNTs and SWNTs with different chiral indices: (10, 2) and (8, 7) measured under excitation at 1.70 eV. The solid (DWNTs) and dashed (SWNTs) lines represent the single exponential decay curves $\text{exp}\left(-\tau /{\tau }_{\text{PL}}\right)$. The upward direction on the vertical axis indicates that the FEC signals have negative sign.

Figure 4

(Color online) PL lifetimes ${\tau }_{\text{PL}}^{\text{DWNT}}$ and ${\tau }_{\text{PL}}^{\text{SWNT}}$ as a function of tube diameter in the DWNTs and SWNTs are denoted by solid circles and squares, respectively. The solid line shows the theoretically calculated curve using Eq. (3). The inset shows the PL lifetime ratio of DWNTs to SWNTs ${\tau }_{\text{PL}}^{\text{DWNT}}/{\tau }_{\text{PL}}^{\text{SWNT}}$ as a function of the tube diameter.