Structural dependence of carbon nanotube orbital magnetic susceptibility: tight binding calculations

Recent ab initio calculations of the orbital magnetic susceptibility anisotropies in carbon nanotubes (CNTs) have shown large, systematic differences among zigzag CNTs of similar diameters [1]. We theoretically investigate the origin of these trends by applying the zone-folding method within the nearest-neighbor tight-binding approximation to all chiral and achiral semiconducting CNT species with diameters between 0.6 nm and 1.7 nm. Our results show qualitative agreement with the ``mod 1'' and ``mod 2'' trends of the ab initio theory and additionally distinguish between trigonal warping and curvature-related effects as physical reasons for the predicted species-dependent spread. Our calculations show (2n+m) patterns similar to those in a recent, experimentally-motivated ``fan-out'' diagram [2] and can be likewise fit to an analytical four-term chirality expansion. [1] Marques, M. A. L.; d'Avezac, M. {\&} Mauri, F.,\textit{ Phys. Rev. B, }\textbf{2006}$, 73$, 125433 [2] Torrens, O. N.; Milkie, D. E.; Ban, H. Y.; Zheng, M.; Onoa, G. B.; Gierke, T. D. {\&} Kikkawa, J. M., \textit{J. Am. Chem. Soc., }\textbf{2007}$, 129$, 252-253