Dielectric Screening inside Carbon Nanotubes

Abstract

Dielectric screening plays a vital role in determining physical properties at the nanoscale and affects our ability to detect and characterize nanomaterials using optical techniques. We study how dielectric screening changes electromagnetic fields and many-body effects in nanostructures encapsulated inside carbon nanotubes. First, we show that metallic outer walls reduce the scattering intensity of the inner tube by 2 orders of magnitude compared to that of air-suspended inner tubes, in line with our local field calculations. Second, we find that the dielectric shift of the optical transition energies in the inner walls is greater when the outer tube is metallic than when it is semiconducting. The magnitude of the shift suggests that the excitons in small-diameter inner metallic tubes are thermally dissociated at room temperature if the outer tube is also metallic, and in essence, we observe band-to-band transitions in thin metallic double-walled nanotubes.

Keywords: carbon nanotubes; dielectric screening; double-walled nanotubes; excitons; one-dimensional heterostructures; resonant Raman.

Figure 1

Dielectric screening in DWCNTs. (a) Model of a DWCNT as a cylinder of two dielectric walls. The EM field at the position of the inner tube is modulated by the outer wall dielectric constant. (b) The dielectric effect manifests in the resonant Raman profiles of the (n₀, m₀) inner wall (blue) compared to corresponding SWCNT (black) computed by eq 4. The profile of DWCNTs is red-shifted due to exciton screening, and the amplitude is reduced by the local field factor compared to that of the SWCNT.

Figure 2

Radial breathing modes in M@M (blue) and M@S (purple) nanotubes excited with a 2.1 eV laser. (a) RBM spectra in the region between 100 and 400 cm^–1. The top line roughly divides expected RBMs from metallic (blue) and semiconducting (orange) walls. Inner wall RBM fitting in the (b) M@S sample and (c) M@M sample. The vertical lines divide different 2n + m laola families. The arrow indicates the increase in the chiral angle within a laola group.

Figure 3

Electromagnetic field screening in the M@M sample. (a–c) Relative intensities of the RBMs originating from the inner and outer walls in S@S, M@S, and, M@M samples, respectively. The inner and outer walls excited at different energies are separated by a vertical line at 200 cm^–1. (d) Resonant Raman profile of the inner (12,0)@M and outer M@(12,12) wall, with RBMs at 249  and 144 cm^–1, respectively. Symbols are experimental data, and lines are fits by eq 4. (e) Green bars: measured Raman intensities (M_R²) as a function of wall diameter, estimated from resonant Raman profiles (note the logarithmic scale of the y axis). Red line: calculated Raman intensity ε_oT = 10 and ε_oT = 1, by eq 1. Gray line: intrinsic M_R² without the correction factor.

Figure 4

Exciton screening in the S@M and M@M samples studied by resonant Raman scattering. Resonant Raman profiles of (a) (11,2)@M and (b) (11,2)@S. Symbols represent experimental data, and lines fits by eq 4. The positions of the transition energies are marked by vertical lines. (c) Transition energy shifts measured in the identical inner tubes in the M@M and M@S samples (listed in Table 1). The inset shows diameter dependence ε_eff vs the outer wall diameter for ε_oT and ε_i values of 10 and 1, respectively.