Polarized Raman Spectra of Carbon Nanotubes
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Ado Jorio , Sandra D. M. Brown , Gene Dresselhaus , Mildred S. Dresselhaus ,
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Marcos A. Pimenta , Riichiro Saito , Apparao M. Rao , and Katrin Kneipp
Massach usettsInstitute of T ec hnology,Cambridge, MA 02139-4307; Univ. F ederal deMinas Gerais, Belo Horizonte, MG 30123-970 Brazil; c Univ. of Electro-Communications, Tokyo, 182-8585 Japan; d Clemson Universit y,Clemson, SC 29634-0978 e Technical Universit yof Berlin, Berlin, 10623, Germany a
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ABSTRACT
P olarizedresonant Raman spectra for the G-band were obtained from a rope of aligned semiconducting SWNTs and from nonaligned semiconducting and metallic SWNTs. Based on group theory analysis and related theoretical predictions, we assign the symmetry for the modes in the G-band of both metallic and semiconducting SWNTs. The frequency shifts of the tangential G modes from the 2D graphite-like E2g frequency are discussed in terms of the nanotube geometry. 2
INTRODUCTION
Raman scattering has been extensively used to study the 1D characteristics of (n; m) carbon nanotubes and to characterize their geometric structure[1]. Due to the folding of the graphite Brillouin zone into the single wall carbon nanotube (SWNT) zone and due to the nanotube curvature, the E2g tangential vibration in graphite splits into sev eralmodes with di erent symmetries in SWNTs, giving rise to a complex G-band feature. This G-band feature has been largely used to study and describe the SWNTs, mainly due to the major di erence of its lineshape for metallics and semiconducting SWNTs.[1] Howev er,various authors used di erent number of modes to analyze this feature, making it diÆcult to compare the results reported b ydi erent groups and to understand the physics behind this feature.[1] Here we summarize resonant Raman polarization results for aligned semiconducting SWNTs, and for a sample of non-aligned SWNTs, with both semiconducting and metallic tubes resonant. We show that it is possible to make symmetry assignments for the normal modes in one-dimensional materials using di erent polarization geometries, and we discuss the unique identi cation of the symmetry of the 6 Raman active G-band modes in carbon nanotubes bundles. We discuss the di erences in the G-band for metallic and semiconducting SWNTs, and the frequency shifts of the tangential G modes from the 2D graphite-like E2g frequency are discussed in terms of the nanotube geometry. 2
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GROUP THEORY FOR THE
G-BAND
IN SWNTs
Although the presence of nanotube-nanotube in teractions may cause some changes in the vibrational behavior of SWNTs in bundles, including symmetry breaking e ects, these interactions havebeen shown not to be important for the G-band Raman spectra of SWNTs under ambient conditions[1], so that the free nanotube symmetries (Dnh, Dnd or CN= [1]) can be used. According to group theory analysis, six modes can be present in the G band of A6.5.1
Group Theory A
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+
−
−
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basis function
E1
E2 −
+ +
−−
+ +
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D nd D nh D N/Ω
(x + y ), z
A1g A1g
A
xz, yz
E 1g E 1g
E1
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