Mapping excitons in semiconducting carbon nanotubes with plasmonic nanoparticles

We develop a consistent theoretical framework suited for the description of confined-exciton mapping in semiconducting carbon nanotubes, using apertureless scanning near-field optical microscopy. In the proposed experimental setup, a plasmonic nanoparticle, such as a nanosphere, is scanned over the nanotube, and the scattered light is recorded. The presence of the plasmonic nanoparticle modifies the excitation channel as well as the dielectric environment, which can be exploited to extract information about the confined excitons. From our simulations, we identify characteristic features observable in experiment.

Figure 1

Schematics of the mapping of CNT excitons with a plasmonic nanoparticle. In the lower part of the panels, we depict our generic boxlike confinement potential and the confined exciton states. In the upper part, we sketch the electric-field distribution produced by the surface plasmons of the metallic nanoparticle. (a) For light polarization parallel to the nanotube symmetry axis, the CNT exciton can be directly excited or via the nanoparticle. The arrows indicate the dipole moments of the nanoparticle and the exciton. (b) For perpendicular light polarization, the exciton can only be excited via the plasmonic nanoparticle. The near fields of the nanoparticle, schematically shown in the figure, are such that the induced exciton dipole moments on the left- and right-hand side of the nanoparticle point into opposite directions.

Figure 2

Simulated light-scattering spectra for the setup depicted in Fig. 1 and for light polarization (a,c) parallel and (b,d) perpendicular to the CNT symmetry axis, and for a nanoparticle-CNT distance of (a,b) 5 nm and (c,d) 10 nm. We plot the normalized spectra and use a logarithmic color scale. For the smaller distance, panels (a,b), we observe a pronounced redshift of the scattering peaks when the plasmonic nanoparticle comes close to the confined exciton.

Figure 3

Real part of polarization ${\mathcal{P}}_z(z)$ (i.e., “exciton wave function”) in arbitrary units, as obtained from our simulations, at the scattering maxima of lowest energy in the trap center (photon energies are given in the panels) and for different nanoparticle positions. The setups for the different panels correspond to those of Fig. 2, and the dashed lines indicate the positions of the metallic nanoparticle. For parallel light polarization and a small MNP-CNT distance, panel (a), we observe an attractive interaction (due to the induced image dipole), and the maximum of ${\mathcal{P}}_z(z)$ follows the plasmonic nanoparticle. (b) For perpendicular polarization, the wave function has a node below the plasmonic nanoparticle, as a result of the excitation via the surface-plasmon fields depicted in Fig. 1b.