Direct Measurement of Strain-Induced Changes in the Band Structure of Carbon Nanotubes

The electronic properties of carbon nanotubes are uniquely sensitive to geometry, with either semiconducting or metallic band structure possible, depending on the exact (n, m) chiral indices [1]. A consequence of this sensitivity is the existence of strong and unusual electromechanical effects whose magnitude and sign are predicted to depend on the chiral indices [2 ‐6]. Previous experimental studies [7‐11] have provided qualitative confirmation of theoretical predictions, but quantitative comparison has been difficult because of a lack of independent knowledge of the nanotube crystal structure. Accurate determination of these effects is important for nanotube electromechanical devices, as well as understanding of electron-phonon scattering and environmental perturbations. In this Letter, we present measurements of straininduced changes in the electronic structure of individual single-walled carbon nanotubes (SWNTs). The shifts are qualitatively consistent with existing theory. At the quantitative level, however, previous theoretical treatments significantly overestimate the strain-induced energy shifts. Through a modification of the earlier treatment to account for sublattice relaxation using existing atomic interaction potentials, we obtain excellent agreement with experiment without the introduction of any adjustable parameter. Rayleigh scattering spectroscopy [12], which measures the frequency-dependent scattering of white light from a single freely suspended nanotube, was used for the precise measurement of the effect of strain on the optical transition energies, as well as for identification of the nanotube crystal structure. For the nanotubes studied in this work (with diameters of 2.1‐2.4 nm) and the available spectral range, we observed scattering peaks corresponding to the third and fourth optical transitions (S33 and S44) for semiconducting nanotubes and the second optical transition (M22) for metallic ones. The positions of these peaks permit the determination of unique (n, m) indices for the spectra. The assignments are based on previous studies that employed independent structural determination by electron diffraction [13] and are also consistent with Kataura plot patterns found by photoluminescence and resonant Raman spectroscopy [14,15]. Because Rayleigh spectroscopy requires suspended samples to eliminate background optical signal, previous studies have used SWNTs grown over slits etched through Si wafers [12] with a thin Si3N4 epilayer. In this work, the single slit was replaced by an ‘‘H’’ shape [Fig. 1(a)]. Chemical vapor deposition was used to grow long (� mm total length) nanotubes that aligned with the CVD gas flow and spanned the � 100 � m wide central slit. The sample growth procedure and geometry have been described in