Intersubband Edge Singularity in Metallic Nanotubes

The tunneling density of states of both the massless and massive (gapped) particles in metallic carbon nanotubes is known to have an anomalous energy dependence. This is the result of coupling to multiple low-energy bosonic excitation (plasmons). For both kinds of particles the ensuing effect is the suppression of the density of states by electron-electron interactions. We demonstrate that the optical absorption between gapless and gapped states is affected by the many-body effects in the opposite way. The absorption probability is enhanced compared with the noninteracting value and develops a power-law frequency dependence, $A(\omega )\propto (\omega -\Delta {)}^{-\gamma }$, where $\gamma \approx 0.2$ for typical nanotubes.

Figure 1

Processes responsible for the optical absorption in metallic nanotubes. (a) Polarization along the NT axis: only transitions with no change of the angular momentum, $m\to m$, are allowed (except $0\to 0$). The $E_{11}$ transition is indicated by the dashed line, the transition threshold $\omega =2\Delta$. (b) Polarization perpendicular to the NT axis: $m\to m\pm 1$ is required. The processes involving right-moving massless particles are indicated. At zero temperature $T=0$ the $E_{01}$ and $E_{10}$ transitions are contributing to the optical absorption. The transition threshold $\omega =\Delta$.