Magneto-optical spectroscopy of highly aligned carbon nanotubes: Identifying the role of threading magnetic flux

We have investigated excitons in highly aligned single-walled carbon nanotubes (SWCNTs) through optical spectroscopy at low temperatures down to 1.5 K and high magnetic fields $\left(\mathit{B}\right)$ up to 55 T. SWCNT/polyacrylic acid films were stretched, giving SWCNTs that are highly aligned along the direction of stretch $\left(\widehat{n}\right)$. Utilizing two well-defined measurement geometries, $\widehat{n}\parallel \mathit{B}$ and $\widehat{n}\perp \mathit{B}$, we provide unambiguous evidence that the photoluminescence energy and intensity are only sensitive to the $\mathit{B}$-component parallel to the tube axis. A theoretical model of one-dimensional magnetoexcitons, based on exchange-split “bright” and “dark” exciton bands with Aharonov-Bohm-phase-dependent energies, masses, and oscillator strengths, successfully reproduces our observations and allows determination of the splitting between the two bands as $\sim 4.8\text{meV}$ for (6,5) SWCNTs.

Figure 1

(Color online) Contour plots of PL intensity as a function of magnetic field with nanotubes aligned (a) parallel $\left(\widehat{n}\parallel \mathit{B}\right)$ to and (b) perpendicular $\left(\widehat{n}\perp \mathit{B}\right)$ to the magnetic field. As the magnetic field increases, the PL peak shifts and increases in intensity.

Figure 2

(Color online) (a) PL spectra at 0 and 55 T with $\widehat{n}\parallel \mathit{B}$ and $\widehat{n}\perp \mathit{B}$. At zero field, both configurations have the same spectra (black solid). At high field, the intensity is increased and emission energy redshifted for $\widehat{n}\parallel \mathit{B}$ (red/dark gray solid) much more than for $\widehat{n}\perp \mathit{B}$ (blue/light gray dashed). (b) Absorption spectra at 0 and 55 T in the same configurations. The intensity is decreased and the peak broadened (integrated oscillator strength is conserved) for $\widehat{n}\parallel \mathit{B}$ (red solid) while $\widehat{n}\perp \mathit{B}$ (blue dashed) is unchanged.

Figure 3

(Color online) PL peak shift (a) and normalized peak area (b) as a function of the SWCNT-parallel component of $\mathit{B}$ $\left(B_{\parallel }\right)$ for $\widehat{n}\parallel \mathit{B}$ (red/dark gray vertical diamonds) and $\widehat{n}\perp \mathit{B}$ (blue/light gray horizontal diamonds). The peak energy matches exactly for both geometries. The peak area matches very well, except for a slight mismatch at high fields. Insets are the same values as a function of total field strength $\left(B\right)$.

Figure 4

(Color online) Experimental (red/dark gray diamonds) and calculated (black solid and dashed lines) peak energy as a function SWCNT-parallel component of magnetic field. Values of ${\Delta }_x$ and $\mu$ were determined from fitting the high-field region of the experimental data and used to calculate the dark and bright magnetoexciton energy. Inset: dispersions energy-level diagram of the four lowest-energy singlet excitons with allowed (circle) and forbidden (crosses) transitions. GS: ground state.