Magnetic field effects on the excitonic absorption spectra of semiconducting single-walled carbon nanotubes

We have investigated the magnetic field effects on the electronic structure and absorption spectra of semiconducting single-walled carbon nanotubes (S-SWCNTs) within a Coulomb correlated $\pi$-electron model. \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402(2004).} \footnote{Z. Wang, H. Zhao, and S. Mazumdar, Phys. Rev. B {\bf 74}, 195406 (2006).} We consider magnetic field parallel to the nanotube axis, which introduces the Aharonov-Bohm phase in the wavefunction. Recent experiments claim to have observed the energy shift and splitting due to the magnetic fields \footnote{S. Zaric {\it et al.,} Phys. Rev. Lett. {\bf 96}, 016406 (2006).} Some of our theoretical results are substantively different from existing results. Comparison with recent experiments are made.