Mechanism for the Compressive Strain Induced Oscillations in the Conductance of Carbon Nanotubes

We report on the monotonic increase and the oscillation of electrical conductance in multiwalled carbon nanotubes with compressive strain. Combined experimental and theoretical analyses confirm that the conductance variation with strain is because of the transition from $s{p}^2$ to $s{p}^3$ configurations that are promoted by the interaction of walls in the nanotubes. The intrawall interaction is the reason for the monotonic increase in the conduction, while the oscillations are attributable to interwall interactions. This explains the observed electromechanical oscillation in multiwalled nanotubes and its absence in single-walled nanotubes, thereby resolving a long-standing debate on the interpretation of these results. Moreover, the current carrying capability of nanotubes can be enhanced significantly by controlling applied strains.

Figure 1

(a) Schematic diagram of the experimental setup. (b) SEM image of an MWCNT array before compression. (c) SEM image of an MWCNT array after compression showing the buckling starting at one end, while the other end remains unaltered. (d) Zoomed SEM image of the buckled region.

Figure 2

(a) $I\mathrm{\text{−}}V$ characteristics taken at the successive compression. The bottom- and top-most curves represent the uncompressed and the most compressed arrays, respectively. Inset: $I\mathrm{\text{−}}\epsilon$ at different voltages. (b) Normalized $I\mathrm{\text{−}}\epsilon$ curve, where almost all the lines fall together. $I\mathrm{\text{−}}\epsilon$ curve fitted with an empirical relation is shown in the inset. (c) $I\mathrm{\text{−}}\epsilon$ curve measured at a step of $\epsilon =0.001$. A small region is extended and shown in the inset. (d) $I\mathrm{\text{−}}\epsilon$ curve showing reversibility, colors of the curves represent different constant voltages.

Figure 3

(a) The supercell of one of the DWCNTs under different strain conditions. Cross-sectional view of DWCNT1 (diameter of 25.37 Å) under various $\epsilon =0.0$, 0.6, and 0.11. The side view of the structure with $\epsilon =0.11$ is also shown. (b) Change in band gap as a function of radial strain for DWCNT1 to DWCNT5. Inset: Threshold strain after which oscillation starts as a function of diameter inverse of the DWCNTs. (c) Similar to (b), for SWCNT of diameter 46.78 Å and band gap variation of a bilayer $AA$ stacked graphene as a function of vertical strain. Inset: Atomic structure of $AA$ stacked bilayer graphene. The band structures are calculated on a $1\times 1\times 20$ K-grid.

Figure 4

(a) Highest occupied molecular orbital and (b) lowest unoccupied molecular orbital wave function (green for positive and magenta for negative) of unstrained DWCNT2 (diameter of 34.89 Å). (c) and (d) show similar plots for the same DWCNT under a strain of 0.03. Isovalue was taken as 0.002 for all the plots. (e) Raman spectra with two different compressive strains. Inset shows the relative shifts in the peak position. (f) Relative peak positions. (g) Intensity ratios of $G$ to $D$ (green curve), $G^{\prime }$ to $D$ (red curve), and $G$ to $G^{\prime }$ (blue curve) with strain.