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

The effect of uniaxial strain on the optical transition energies of single-walled carbon nanotubes with known chiral indices was measured by Rayleigh scattering spectroscopy. Existing theory accurately predicts the trends in the measured strain-induced shifts, but overestimates their magnitude. Modification of the analysis to account for internal sublattice relaxation results in quantitative agreement with experiment.

Figure 1

Schematic representation of the device structure (not to scale). (a, top view) SWNTs are grown across the middle of an H-shaped slit in a Si wafer, and clamped at the ends by gold films. The Si chip is glued to a piece of steel with two attachment pads. The Si chip is then cut along the dashed lines to separate the two halves of the wafer. (b, side view) Light for Rayleigh scattering is focused on a suspended SWNT from the top; the scattered light is collected after passing through the slit and a hole in steel plate (not visible). Typical values for the slit width $w$ and the chip length $L$ were $100\mu \mathrm{m}$ and 12 mm, respectively.

Figure 2

Rayleigh scattering spectra for nanotubes under axial strain, displaced vertically by a distance corresponding to the applied strain. The gray line traces the shift in the transition energy. Results are shown for (a) a semiconducting (20,12) nanotube, (b) a (19,13) chiral metallic nanotube, and (c) a (16,16) armchair metallic nanotube.

Figure 3

Shift rates for the measured nanotube electronic transitions, plotted against the parameter $\mathrm{sgn}(2p+1)(-1{)}^{k+1}\cos (3\theta )$ that is expected to normalize for the nanotube structure and for the optical transition number $k$. The solid squares show experimental results for the all accessible transitions in the 5 measured nanotubes. The existing theoretical prediction [Eqn. (3)] is shown as a solid line, with the modified theoretical prediction [Eqn. (6)] as a dashed line.