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Circular Dichroism of Single Wall Carbon Nanotubes

Saito, Riichiro (Tohoku University, Sendai, JPN); Sato, Naomichi (Tohoku University, Sendai, JPN); Tatsumi, Yuki (Tohoku University, Sendai, JPN)

Recently, single wall carbon nanotubes (SWNTs) can be purified into not only a single chirality specified by two integers (n,m) but also left or right handness of a SWNT (or enantiomers). Depending on handness of the purified SWNTs, Kataura et al. and other group have showed that circular dichroism (CD) appears as a function of wavelength. For left and right handed single chirality SWNT, they show that (1) the sign of CD values alternate plus and minus as a function of the wavelength at Eii energy positions and that (2) at the same Eii, the opposite signs of the CD values appear for left and right handed SWNTs. In this paper, we present a new theory for CD especially for SWNTs. The effect of CD is defined by the different optical absorption of a material for incident left and right circular lights. CD can be generally observed by molecules that have enantiomers. If we simply use the conventional theory of CD for molecules, the calculated CD values gives zero since the CD value that is integrated around the K point in the Brillouin zone exactly cancels that around the K’ point due to the time-reversal symmetry for the electronic structure. This time-reversal symmetry is very robust for any possible lattice deformation and thus conventional theory for CD does not work at all. In the present work, however, a new formalism beyond so-called dipole approximation works well for obtaining the CD values of SWNTs. The analytic and numerical results of the CD values well reproduce the above experimental results. Thus we believe that this work gives an important step for understanding chirality dependent optical properties especially for SWNT enantiomers.

This work is partially supported by MEXT grant (Nos. 25286006, 25107005) Corresponding author: Riichiro Saito e-mail: rsaito@flex.phys.tohoku.ac.jp web: flex.phys.tohoku.ac.jp/japanese tel: +81-022-795-7754

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