Excitons in metallic carbon nanotubes with Aharonov-Bohm flux

Exciton effects in metallic carbon nanotubes with and without magnetic flux are studied in an effective-mass approximation. For parallel polarization, an exciton associated with the first excited bands has an appreciable binding energy even in the presence of strong screening of linear bands. The Aharonov-Bohm splitting of the exciton peak is slightly enhanced due to interaction effects. An Aharonov-Bohm gap in the linear bands is strongly enhanced, but the exciton binding energy tends to largely cancel this enhancement. For perpendicular polarization, there is essentially no exciton effect due to the absence of backscattering within linear bands and interband absorption is nearly suppressed by the depolarization effect.

Figure 1

Schematic illustrations of (a) a 2D graphite sheet and (b) carbon nanotube.

Figure 2

Energy dispersions of a metallic nanotube at (a) $\phi =0$ and (b) 0.1. Numbers denote band index $n$. Arrows in $k<0$ and $k>0$ indicate optical interband transitions for parallel and perpendicular polarizations, respectively. The transition between the linear bands with $n=0$ in (a) is not allowed.

Figure 3

Dynamical conductivity for parallel polarization at (a) $\phi =0.001$ and (b) 0.01. Arrows indicate edges of the bands for $n=\pm 1$ and numbers denote band index $n$. The phenomenological energy broadening $\Gamma {(2\pi \gamma ∕L)}^{-1}=0.005$ (solid lines), 0.02 (dotted liens), and 0.08 (dashed lines) are used.

Figure 4

Magnetic-flux dependence of the exciton energies for the bands with $n=\pm 1$ for parallel polarization is plotted by solid lines. The band edges with and without the Coulomb interaction are drawn by dashed and dotted lines, respectively. Numbers denote band index $n$.

Figure 5

Magnetic-flux dependence of the binding energies of excitons and self-energy shift of the band edges with $n=-1$ (solid lines) and 1 (dashed lines) for parallel polarization.

Figure 6

Coulomb-interaction dependence of the exciton energy (solid lines) and band edge (dashed lines) for the bands with $n=\pm 1$ for parallel polarization in the limit of zero magnetic flux.

Figure 7

Coulomb-interaction dependence of the exciton energies (solid lines) and band edges (dashed lines) for parallel polarization for the bands with $n=\pm 1$ of metallic tubes and for the lowest and second lowest excitations of semiconducting tubes.

Figure 8

Dynamical conductivity for parallel polarization near an AB band gap at $\phi =0.025$. An arrow indicates the band edge for $n=0$. Interband coupling is neglected in the calculations.

Figure 9

Magnetic-flux dependence of the exciton energy (solid lines) and band edge (dashed lines) for the bands with $n=0$ for parallel polarization. The band edge in the absence of the interaction is plotted by a dotted line.

Figure 10

Coulomb-interaction dependence of the coefficient $C$ of the exciton energy (solid lines) and band edge (dashed lines) for the bands with $n=0$ for parallel polarization.

Figure 11

Dynamical conductivity for perpendicular polarization at (a) $\phi =0.001$ and (b) 0.01. Solid and dashed lines denote spectra with and without the depolarization effect, respectively.

Figure 12

Coulomb-interaction dependence of energy broadening of the excitons for the bands with $n=\pm 1$ for parallel polarization.