Mechanism of the Far-Infrared Absorption of Carbon-Nanotube Films

The far-infrared conductivity of single-wall carbon-nanotube ensembles is dominated by a broad absorption peak around 4 THz whose origin is still debated. We observe an overall depletion of this peak when the nanotubes are excited by a short visible laser pulse. This finding excludes optical absorption due to a particle-plasmon resonance and instead shows that interband transitions in tubes with an energy gap of $\sim 10\mathrm{meV}$ dominate the far-infrared conductivity. A simple model based on an ensemble of two-level systems naturally explains the weak temperature dependence of the far-infrared conductivity by the tube-to-tube variation of the chemical potential.

Figure 1

Schematic of proposed mechanisms explaining the far-infrared absorption of NTs. (a) Interband transitions across the band gap $G$ of a small-gap NT. An impurity-assisted intraband transition in the band structure $ϵ(k)$ is also shown. (b) Particle-plasmon resonance. The probing electric field $\mathit{E}$ induces charges on the NT surface which lead to an additional repulsive force on the electrons inside.

Figure 2

Experimentally determined FIR conductivity of the (a–c) unexcited and (d–f) excited NT sample. (a) Real part of the equilibrium conductivity. Different symbols indicate different combinations of THz-generation and detection crystals. (b) Corresponding real part of the dielectric function. (c) $\mathrm{Re}{\sigma }_{\infty }$ as a function of ambient temperature $T_{\mathrm{amb}}$ together with a fit according to Eq. (3). (d, e) Pump-induced changes in the sample conductivity and dielectric function at several pump-probe delays $\tau$. (f) $\mathrm{Re}\Delta {\sigma }_{\tau }$ as a function of the pump fluence.

Figure 3

Theoretical results for the FIR conductivity of a NT ensemble. (a) Modeled $\mathrm{Re}\sigma$ versus electronic temperature $T$ for various standard deviations $\Delta \mu$ of the chemical potential according to Eq. (3). (b) Effect of convoluting the Fermi function $f_{\mu T}$ with a Gaussian distribution $p_{\mu }$ of the chemical potential. The resulting $⟨f_{\mu T}⟩$ is much less temperature dependent. (c, d) Heat-induced change in conductivity and dielectric function as calculated from Eq. (3) and $\mathrm{Re}{\sigma }_{\infty }$ for several electronic temperatures $T$. Note the good qualitative agreement with the experimental data in Figs. 2d, 2e.