Cross-polarized optical absorption of single-walled nanotubes by polarized photoluminescence excitation spectroscopy

Cross-polarized absorption peaks of isolated single-walled carbon nanotubes (SWNTs) were observed by polarized photoluminescence excitation (PLE) spectroscopy. Using a simple theory for PL anisotropy, the observed PLE spectra are decomposed into “pure” components of the photoexcitation for incident light polarized parallel and perpendicular to the SWNT axis. For several $(n,m)$ SWNTs, distinct peaks corresponding to perpendicular excitation were observed. The measured transition energies for perpendicular excitations were blueshifted compared to the qualitative values predicted within a single-particle theory. The results indicate a smaller exciton binding energy for perpendicular excitations than for parallel excitations.

Figure 1

(Color online) Schematics of optical transitions in SWNTs corresponding to (a) collinear and (b) perpendicular absorption and emission dipoles. Solid and dotted arrows indicate $\Delta \mu =0$ and $\Delta \mu =\pm 1$ transitions, respectively. (c) Schematic diagram for the measurement of PL anisotropies of randomly oriented SWNTs.

Figure 2

(Color online) [(a) and (b)] PL and (c) anisotropy maps in the emission energy range of $1.15–1.31\mathrm{eV}$. (d) PLE spectra of (7, 5) SWNTs for $I_{VV}$ and $I_{VH}$ configurations. The $I_{VH}$ spectrum in (d) is magnified $(\times 2)$ and offset for comparison. Peaks marked with $E_{ii}Ph$ $(i=1,2)$ denote phonon-sideband peaks (Refs. 16, 17, 18, 28). PL peaks marked with asterisks (*) in (b) and (d) are the same peak, which corresponds to an area indicated by an oval mark in (c).

Figure 3

(Color online) Decomposed PL maps for (a) collinear $\left(I_{\Vert }\right)$ and (b) perpendicular $\left(I_{\perp }\right)$ dipoles. Dotted lines in (a) and (b) indicate the emission energies of respective SWNTs. Solid lines indicate the position of Raman lines for $G$ and $G^{\prime }$ bands (Ref. 1). Peaks for $I_{\perp }$ spectra are indicated by arrows. Decomposed PLE spectra of (6, 5) and (7, 5) SWNTs for (c) collinear $\left(I_{\Vert }\right)$ and (d) perpendicular $\left(I_{\perp }\right)$ dipoles. The PLE spectra for (6, 5) SWNTs are magnified $(\times 2)$ and offset for comparison in (c) and (d).

Figure 4

(Color online) [(a) and (b)] PL and (c) anisotropy maps in the emission energy range of $1.03–1.15\mathrm{eV}$. Decomposed PL maps for (d) collinear $\left(I_{\Vert }\right)$ and (e) perpendicular $\left(I_{\perp }\right)$ dipoles. Dotted lines in (d) and (e) indicate the emission energies of respective SWNTs. Solid lines indicate the position of Raman lines for the $G^{\prime }$ band (Ref. 1). In (e) PL peaks for $I_{\perp }$ spectra are indicated by arrows.

Figure 5

(Color online) (a) Observed peak positions in PLE spectra for several $(n,m)$ types. Symbols in parentheses are ambiguous by approximately $\pm 40\mathrm{meV}$ due to overlap of other large PL peaks. (b) Calculated transition energies for $\Delta \mu =0$ (black cross) and $\Delta \mu =\pm 1$ (red circle) transitions within TB approximation.