  Low-dimensional carbon nanostructures, such as single-wall carbon nanotubes
(SWCNTs) and graphene, offer new opportunities for terahertz science and
technology. Being zero-gap systems with a linear, photon-like energy
dispersion, metallic SWCNTs and graphene exhibit a variety of extraordinary
properties. Their DC and linear electrical properties have been extensively
studied in the last decade, but their unusual finite-frequency, nonlinear,
and/or non-equilibrium properties are largely unexplored, although they are
predicted to be useful for new terahertz device applications. Terahertz dynamic
conductivity measurements allow us to probe the dynamics of such photon-like
electrons, or massless Dirac fermions. Here, we use terahertz time-domain
spectroscopy and Fourier transform infrared spectroscopy to investigate
terahertz conductivities of one-dimensional and two-dimensional electrons,
respectively, in films of highly aligned SWCNTs and gated large-area graphene.
In SWCNTs, we observe extremely anisotropic terahertz conductivities, promising
for terahertz polarizer applications. In graphene, we demonstrate that
terahertz and infrared properties sensitively change with the Fermi energy,
which can be controlled by electrical gating and thermal annealing.
