Pressure Control of Conducting Channels in Single-Wall Carbon Nanotube Networks

We measure electrical transport on networks of single-wall nanotube ropes as a function of temperature $T$, voltage $V$, and pressure up to 22 GPa. We observe Luttinger liquid (LL) behavior, a conductance $\propto T^{\alpha }$, and a dynamic conductance $\propto V^{\alpha }$. With pressure, conductance increases while $\alpha$ decreases, enabling us to test the theoretical prediction for LL behavior on the $\alpha$ dependence of the $T$ and $V$ independent coefficient of the tunneling conductance, and to obtain the high frequency cutoff of LL modes. The possible transition to a Fermi liquid at $\alpha \to 0$ is unattainable, as nanotubes collapse to an insulating state at high pressures.

Figure 1

Temperature dependence of the conductance of sample $A$ for different pressures. We observe a power law behavior (dashed line) at low temperatures that extends to all temperature at high pressures.

Figure 2

Scaling of the dynamical conductivity of sample $A$ at a pressure of 10 GPa. We observe that the curves for all temperatures collapse to the same curve that has a $V^{\alpha }$ dependence at high bias. Inset: same but as measured dynamical conductance curves at different temperatures.

Figure 3

Pressure dependence of the ${\alpha }^{-1}$ parameter. We use two scales: left for the higher ${\alpha }^{-1}$ values sample $A$ and right for the other, that coincide at the convergence coordinate of their dependences. We observe a linear variation for all samples that converges to the previously measured value of ${\alpha }_{\mathrm{bulk}-\mathrm{bulk}}^{-1}$ at zero pressure. The dashed fit on sample $C$ corresponds to the one obtained with a constant $dn/dP$ under pressure (see text). Sample $A$ shows a phase transition towards a less conducting state at 13 GPa. Inset: variation of the conductance at 1 K of sample $A$ showing the phase transition at 13 GPa.

Figure 4

Relation between the value of the coefficient of the conductance temperature power law with the ${\alpha }^{-1}$ parameter. We observe that all samples fit to the same dependence after normalization with a geometrical factor. The universal fitting factor $\hslash \omega =2.6\pm 0.8\mathrm{eV}$ corresponds to the Fermi energy of the individual nanotubes. Inset: time evolution of the ${\alpha }^{-1}$ parameter of sample $A$ at 22.1 GPa (final pressure). We observe a logarithmic time dependence typical of relaxation in disordered systems.