Dielectric screening effects on transition energies in aligned carbon nanotubes

Abstract

The optical transition energies ${E}_{ii}$ of carbon nanotubes (CNTs) strongly depend on the dielectric function ${\ensuremath{\varepsilon}}_{q}$ of the nanotubes and the dielectric background constant ${\ensuremath{\varepsilon}}_{\mathrm{bg}}$ of their surroundings. It becomes particularly evident when CNTs in solution and free-standing, vertically aligned CNTs are compared via their optical spectra. Using photoluminescence-excitation spectroscopy, we determine the first two transition energies for these two types of carbon-nanotube samples, i.e., for CNT-solution and CNT-forest samples. We observe considerable energy shifts and explain them by microscopic calculations based on the density-matrix formalism. Combining experiment and theory, we determine the dielectric background constant of the CNT-forest and CNT-solution samples to be $1.3\ifmmode\pm\else\textpm\fi{}0.1$ and $1.8\ifmmode\pm\else\textpm\fi{}0.1$, respectively.