Evidence for Dark Excitons in a Single Carbon Nanotube due to the Aharonov-Bohm Effect

We studied exciton structures and the Aharonov-Bohm effect in a single carbon nanotube using micro-photoluminescence (PL) spectroscopy under a magnetic field at low temperatures. A single sharp PL peak from the bright exciton state of a single carbon nanotube was observed under zero magnetic field, and the additional PL of dark exciton state appeared below the bright exciton peak under high magnetic fields. It was found that the split between the bright and dark exciton states is several millielectron volts at zero field. The tube diameter dependence of the splitting arises from the intervalley short-range Coulomb interaction.

Figure 1

(a) PL spectrum of a typical suspended single SWNT [assigned chiral index (7,6)] in comparison with the ensemble-averaged spectrum of micelle-wrapped SWNTs dispersed in gelatin. (b) Polar plot of the PL intensity of a typical single SWNT versus the polarized direction $\theta$ of the excitation laser. The PL data (circle) were fitted using ${cos}^2\theta$ (solid line). (c) Schematic of the directional relationship between the nanotube axis and magnetic field. In this case, the relative angle $\alpha$ was estimated to be about 13°.

Figure 2

(a) Normalized magneto-PL spectra of a single (9,4) carbon nanotube at 20 K in the Voigt geometry ($\alpha \approx 9°$). The split PL spectra are fit by two Lorentzian functions. (b) The normalized magneto-PL spectra of a single (9,5) carbon nanotube at 20 K in the Faraday geometry. The PL spectra are fit by a Lorentzian function. (c) Temporal evolution of the PL spectra with 10 s accumulation time in (a) at 7 T. (d) The energy positions of the bright and dark exciton states as a function of the magnetic field in (a). (e) Splitting energy ${\Delta }_{bd}$ ($B$) versus the magnetic field. The solid line corresponds to the theoretically fitted curve based on Eq. (2).

Figure 3

Magneto-PL spectra obtained from typical single carbon nanotubes for different chiralities in the Voigt geometry. The chralities for (a)–(d) are (9,8), (10,3), (9,5), and (7,5), respectively. The relative angles $\alpha$ for (a)–(d) are about 14°, 10°, 63°, and 28°, respectively.

Figure 4

Tube diameter dependence of the splitting energy between the bright and dark exciton states at zero field. The dotted line corresponds to the theoretically predicted dependence of $1/d^2$.