Ballistic- and quantum-conductor carbon nanotubes: A reference experiment put to the test

We have performed electrical transport experiments on individual carbon nanotubes (CNTs) in situ in a transmission electron microscope using the liquid-metal contact method (LMC method), which consists of immersing a CNT placed on the apex of a metallic tip into a drop of liquid mercury (Hg). In the literature, this method has been mostly employed without visualization (ex situ) to show the ballistic- and quantum-conductance properties of different kinds of CNTs. We show that on the one hand the in situ LMC method is well suited to create low-resistance contacts with the CNTs but on the other hand the ballistic and quantum conductance measured by the ex situ LMC method is likely to give false positives for three reasons: (a) the CNTs are likely to be removed from the tip surface through contact with the Hg, (b) occurring Hg-tip surface nanocontacts are likely to be mistaken for quantum-conductor CNTs, and (c) occurring Hg nanomenisci are likely to be mistaken for ballistic-conductor CNTs. These findings have strong consequences for the interpretation of previously reported works.

Figure 1

Illustration of the liquid-metal contact (LMC) method: (a) resistance-length dependence of diffusive CNTs, (b) schematic drawing of a CNT placed on a metallic tip being immersed into a drop of liquid metal, (c) resistance-length dependence of ballistic CNTs. In (b1), the resistance of the whole CNT is measured, whereas in (b2) only the resistance of the nonimmersed part of the CNT is measured. See text for more explanations.

Figure 2

CNTs on tips: (a) SEM image and (b) TEM image of CNTs on the apices of W tips, (c) SEM image of CNTs on the apex of an AFM tip.

Figure 3

Histograms of Au/CNT-tip and Hg/CNT-tip low-bias contact resistance values. Note the logarithmic resistance scale. The area under the histograms gives the number of CNTs on the respective sample. Upper row: Au/CNT-tip resistance values. Lower row: Hg/CNT-tip resistance values. Left column: Resistance values for all five samples taken on 10 CNTs (for Au) respectively 9 CNTs (for Hg) in contact with different places on the Au (respectively Hg) counterelectrode. Middle column: Resistance values for sample 1 taken on 3 CNTs (for Au) respectively on 2 CNTs (for Hg) in contact with different places on the Au (respectively Hg) counterelectrode. Right column: Resistance values for sample 2 taken on 1 CNT (for Au) respectively on 3 CNTs (for Hg) in contact with different places on the Au (respectively Hg) counterelectrode. Dashed lines indicate the positions of the geometrical average resistances. Resistance values above $1\mathrm{G}\Omega$ have not been considered in the calculation of the geometrical average resistances.

Figure 4

Upper part: the conductance vs time dependence, acquired in situ during cyclic immersion of a tip with CNTs at the apex into the Hg according to the common experimental protocol for ex situ experiments, meets the criteria for ballistic transport and conductance quantification [red: conductance, blue: sample displacement (amplitude: 220 nm)]; lower part: only visual control can tell us that the transport measurement is not being performed on CNTs but on several Hg nanomenisci sticking to the tip surface, the CNTs having been removed by the Hg during previous immersions. The length of the conductance plateaus as expressed in nm is defined as the position of the sample at the beginning of the plateau minus the position of the sample at the end of the plateau.

Figure 5

A Hg meniscus sticking to the apex of the tip. (A) Visualization. (B) Conductance vs time dependence. (a), (b), and (c) designate the moments in (B) at which the corresponding images in (A) were taken. The sample displacement between (a) and (b), and between (b) and (c), is monotonic. During retraction and approach of the tip to the Hg droplet of about 100 nm, the Hg meniscus follows the tip. The conductance varies but the variation is uncorrelated to the mechanical displacement.

Figure 6

Examples of Hg nanomenisci sticking to different places on the tip surface (Hg: black contrast, upper left corner; tip: dark gray contrast, lower right corner) shown in chronological order. Only the maximum values of each contact conductance are taken into account. The conductance values of new small nanocontacts (red circles) are calculated as the difference between two consecutive total conductance values of the Hg nanomenisci. These nanocontact conductance values are always either $0G_0$ or of the order of $G_0$. In particular, image (d) proves that the conductance of a CNT in contact with the Hg droplet can be $0G_0$. Also shown is a particle (diameter $>$ 200 nm), which does not make mechanical contact with the tip surface as it is at a different height. This particle is floating on the Hg surface (thick blue arrow) and has been most likely detached from the tip surface by a Hg immersion.

Figure 7

A CNT rope which bifurcates close to the Hg surface. A thin part of the rope is in contact with a Hg meniscus which appears to be strongly pinned to it and which follows the CNT rope during its retraction from and approach to the Hg droplet of about 30 nm. However, the majority of the CNTs inside the rope lie down on the Hg surface.