Origin of the Background Absorption in Carbon Nanotubes: Phonon-Assisted Excitonic Continuum

TL;DR

This study reveals that the background absorption in semiconducting carbon nanotubes originates from phonon-assisted excitonic transitions, supported by experimental measurements and a detailed theoretical model involving microscopic interactions.

Contribution

The paper introduces a comprehensive theoretical model that explains the background absorption in carbon nanotubes as phonon-assisted excitonic transitions, validated by experimental data.

Findings

Background absorption is due to phonon-assisted transitions to excitonic continuum states.

The theoretical model accurately fits experimental absorption spectra.

The approach can be extended to study out-of-equilibrium dynamics in low-dimensional materials.

Abstract

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.