Influence of nanotube length and density on the plasmonic terahertz response of single-walled carbon nanotubes

We measure the conductivity spectra of thin films comprising bundled single-walled carbon nanotubes (CNTs) of different average lengths in the frequency range 0.3-1000 THz and temperature interval 10-530 K. The observed temperature-induced changes in the terahertz conductivity spectra are shown to depend strongly on the average CNT length, with a conductivity around 1 THz that increases/decreases as the temperature increases for short/long tubes. This behaviour originates from the temperature dependence of the electron scattering rate, which we obtain from Drude fits of the measured conductivity in the range 0.3-2 THz for 10 $mu$m length CNTs. This increasing scattering rate with temperature results in a subsequent broadening of the observed THz conductivity peak at higher temperatures and a shift to lower frequencies for increasing CNT length. Finally, we show that the change in conductivity with temperature depends not only on tube length, but also varies with tube density. We record the effective conductivities of composite films comprising mixtures of WS$_2$ nanotubes and CNTs vs CNT density for frequencies in the range 0.3-1 THz, finding that the conductivity increases/decreases for low/high density films as the temperature increases. This effect arises due to the density dependence of the effective length of conducting pathways in the composite films, which again leads to a shift and temperature dependent broadening of the THz conductivity peak.