  Excitonic effects in 1D semiconductors can be qualitatively different from
those in higher dimensions. In particular, the Sommerfeld factor, the ratio of
the above-band-edge excitonic continuum absorption to free electron-hole pair
generation, has been shown to be less than 1 (i.e., suppressed) in 1D systems
while it is larger than1 (i.e., enhanced) in 2D and 3D systems. Strong
continuum suppression indeed exists in semiconducting single-wall carbon
nanotubes, a prototypical 1D semiconductor. However, absorption spectra for
carbon nanotubes are typically fit with a combination of Lorentzians and a
polynomial background baseline with little physical meaning. Here, we performed
absorption measurements in aligned single-chirality (6,5) carbon nanotube
films. The obtained spectra were fit with our theoretical model obtained by
solving the Boltzmann scattering equation (i.e., the quantum Fokker-Planck
equation), involving fifty-nine different types of transitions among three
different types of quasiparticles. Specifically, we took into account
microscopic interactions between photons, phonons, and excitons, including
their dispersions, which unambiguously demonstrated that the background
absorption is due to phonon-assisted transitions from the semiconductor vacuum
to finite-momentum continuum states of excitons. The excellent agreement we
obtained between experiment and theory suggests that our numerical technique
can be seamlessly extended to compute strongly out-of-equilibrium many-body
dynamics and time-resolved spectra in low-dimensional materials.
