Resonant Raman spectroscopy of individual metallic and semiconducting single-wall carbon nanotubes under uniaxial strain

Uniaxial strain is induced by pushing single-wall carbon nanotubes (SWNTs) with an atomic force microscope tip. The vibrational and electronic energies of nanotubes are found to be very sensitive to strain. For both metallic and semiconducting SWNTs under strain, the $D$, $G$, and $G^{\prime }$ band Raman modes are downshifted by up to 27, 15, and $40{\mathrm{cm}}^{-1}$, respectively. The relative strain-induced shifts of the $D$, $G$, and $G^{\prime }$ bands vary significantly from nanotube to nanotube, implying that there is a strong chirality dependence of the relative shifts. Semiconducting SWNTs remain strongly resonant under these large deformations, while metallic SWNTs appear to move in and out of resonance with strain, indicating a strain-induced shifting of the electronic subbands. Tight-binding calculations of the electronic band structure of semiconducting and metallic nanotubes under uniaxial strain predict significant shifting of the subband energies, leading to strain-induced changes in the Raman intensity. These theoretical predictions are consistent with what we observe experimentally for metallic nanotubes, but not for semiconducting nanotubes.

Figure 1

(Color online) Top: schematic drawing of an AFM tip displacing a nanotube. Bottom: AFM image of a metallic SWNT held fixed at the ends by metal pads. The nanotube was strained by 0.95% with an AFM tip. Some residue remaining at the original position of the SWNT is visible in the AFM image and allows us to image the strained and unstrained lengths simultaneously.

Figure 2

Measured downshifts of the $D$-, $G$-, and $G^{\prime }$-band Raman-mode frequencies of semiconducting SWNTs resonant with a $514\text{−}\mathrm{nm}$ Ar ion laser plotted as a function of strain. Each point on a given plot was taken on a different SWNT.

Figure 3

(Color online) Raman spectra of the metallic SWNT of Fig. 1 measured with a $633\text{−}\mathrm{nm}$ HeNe laser before and after inducing a 0.95% strain.

Figure 4

Joint density of states for a (14,6) semiconducting nanotube and a (16,1) metallic nanotube with and without 1% uniaxial strain.

Figure 5

(Color online) Top: calculated strain-induced shift of the intersubband transitions $E_{11}^M$ and $E_{33}^S$. Bottom: chirality dependence of the shift in $E_{11}^M$ and $E_{33}^S$ under 1% uniaxial strain. Calculations were made on nanotubes in the diameter range $1.1–1.5\mathrm{nm}$.

Figure 6

(Color online) Raman intensity profiles for a (14,6) semiconducting nanotube and a (16,1) metallic nanotube calculated with and without uniaxial strain. The vertical lines indicate the fixed laser energies $2.41\mathrm{eV}$, for semiconducting nanotubes, and $1.96\mathrm{eV}$, for metallic nanotubes.