High Field Magneto-optical Spectroscopy of Semiconducting Single-walled Carbon Nanotubes

Single-walled carbon nanotubes (SWNTs) present an ideal system for study of one dimensional physics. Classically speaking, their long persistence lengths result in rigid-rod-like behavior in the solution-phase. Quantum mechanically speaking, extreme confinement in the radial direction result in interesting properties for optically excited correlated electron-hole pairs, or excitons. In addition, their hollow crystalline structure presents a controllable way to modify the circumferential boundary conditions on their electronic wavefunctions resulting in changes to the electronic band structure via threading a magnetic field through the diameter. An applied magnetic field also aligns SWNTs due to their magnetic susceptibility anisotropy. We have measured the dynamic alignment properties of single-walled carbon nanotube (SWNT) suspensions in pulsed high magnetic fields through linear dichroism spectroscopy. Millisecond-duration pulsed high magnetic fields up to 55 T as well as microsecond-duration pulsed ultrahigh magnetic fields up to 166 T were used. Due to their anisotropic magnetic properties, SWNTs align in an applied magnetic field, and due to their anisotropic optical properties, aligned SWNTs show linear dichroism. The characteristics of their overall alignment depend on several factors, including the viscosity and temperature of the suspending solvent, the degree of anisotropy of nanotube magnetic susceptibilities, the nanotube length distribution, the degree of nanotube bundling, and the strength and duration of the applied magnetic field. In order to explain our data, we have developed a theoretical model based on the time-dependent Smoluchowski equation for rigid rods that accurately reproduces the salient features of the experimental data. We have also investigated excitons in SWNTs in stretch aligned polyacrylic acid films, direction of stretch (n̂), through optical spectroscopy at low temperature (1.5 K) and high magnetic fields (B) up to 55 T. The application of a magnetic field along the SWNT axis drastically increases the measured photoluminescence, by as much as a factor of 6, at low temperatures. To explain this we have developed a theoretical model based on field-dependent exciton band structure and the interplay of Coulomb interactions and the Aharonov-Bohm effect. This conclusively explains our data as the first experimental observation of dark excitons 5-10 meV below the bright excitons. In addition, utilizing two well-defined measurement geometries, n̂ ‖ B and n̂ ⊥ B , we provide unambiguous evidence that the photoluminescence energy and intensity are only sensitive to the B -component parallel to the tube axis.