Resonant hyper-Raman scattering from carbon nanotubes Katsuyoshi Ikeda a,b, * , Yuika Saito b,c , Norihiko Hayazawa b , Satoshi Kawata b,c , Kohei Uosaki a a Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan b RIKEN, Wako, Saitama, 351-0198, Japan c Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan Received 22 December 2006; in final form 10 February 2007 Available online 22 February 2007 Abstract Phonon modes of single-walled carbon nanotubes were observed by means of hyper-Raman scattering. The infrared active G- and D- bands were clearly observed in the spectrum, while no infrared-inactive radial breathing modes were detected. Both one- and two-photon electronic resonances were found to contribute to the scattering intensity enhancement, which suggested the possible utility of hyper- Raman spectroscopy as a unique tool for detection of vibrational modes. Ó 2007 Elsevier B.V. All rights reserved. 1. Introduction Carbon nanotubes (CNTs) have attracted much atten- tion because of their unique electrical, optical, and mechan- ical properties since their discovery in 1991 [1]. These properties depend on their geometrical structure, e.g., diameter, chirality, and aspect ratio [2]. Therefore, spec- troscopic studies of CNTs are especially important from theoretical and experimental viewpoints. Vibrational spec- troscopy is one of the most powerful tools to characterize single-walled carbon nanotubes (SWNTs), because spectral features of phonon modes in SWNTs are directly related to their symmetries (n, m) [2–4]. It has been theoretically pre- dicted that achiral SWNTs (m = n or m = 0) possess 8 Raman-active and 3 infrared (IR) active phonon modes, whereas chiral SWNTs (0 < m 6¼ n) have 14 Raman-active and 6 IR-active ones [2]. As for the Raman-active phonon modes, there have been many experimental reports because SWNTs exhibit very strong resonant Raman scattering (RS) in the visible region [5–7]. On the other hand, there are only few experimental reports on the IR-active phonon modes because of the difficulty in detection [8,9]. The diffi- culty is, in part, because SWNTs do not support a static dipole moment, and hence, much weaker dynamic dipole moment has to be taken into account [8]. Moreover, CNT samples usually contain carbon impurities that may induce similar IR absorption, making IR assignments much more difficult. There is another way to access IR-active phonon modes. Hyper-Raman scattering (HRS), which is due to hyperpo- larizability modulations by nuclear vibrations of molecules, has rather similar selection rules to IR, although HRS is an analogue of RS in the second-order nonlinear optical pro- cesses [10]: b ijk ¼ b 0 ijk þ X l ðob ijk =oQ l Þ 0 Q l þ ; ð1Þ where hyperpolarizability b is represented as the expansion in the series of the normal coordinates Q near the equilib- rium b 0 and the second term is responsible for HRS. Since all the IR-active modes are allowed in HRS [10–12], this nonlinear scattering can in principle be an alternative of IR spectroscopy [13]; note that HRS is allowed even in cen- trosymmetric media. More importantly, electronic reso- nances can contribute to the enhancement of HRS intensity. This is a great advantage, which is never expected 0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.02.050 * Corresponding author. Address: Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan. Fax: +81 11 706 3440. E-mail address: kikeda@pchem.sci.hokudai.ac.jp (K. Ikeda). www.elsevier.com/locate/cplett Chemical Physics Letters 438 (2007) 109–112