Multiwalled carbon nanotubes are ballistic conductors at room temperature

Following the experiments of Frank et al. [1], which demonstrated quantum transport in multiwalled carbon nanotubes, there have been several experiments that appear to contradict the main conclusion of that paper, which is that the transport of a MWNT at room temperature is ballistic. Here we demonstrate that the intrinsic resistance of cleanarc-produced carbon nanotubes is at most 200Ω/μm, which implies that the momentum mean free path is greater than 30 μm, which in turn is much larger than the tube length. This implies that these tubes are ballistic, according to the standard definition of ballistic transport. We also show that the contact resistance with mercury is quite large: a nanotube in contact with Hg over 100 nm of its length still represents a 3000Ω resistance. PACS: 73.22.-f; 72.15.Lh; 73.63.Fg Transport in carbon nanotubes is both fascinating and controversial. Nanotubes have been shown to be (depending on the conditions and environment) both ballistic [1] and diffusive [2–5], and SWNTs appear to be p-doped due to the contact [6] or from atmospheric gasses [7, 8]. They are either metallic or semiconducting depending on the helicity [9]. Frank et al. [1] demonstrated several important transport properties in arc-produced MWNTs in a very simple experiment that involved contacting the nanotubes by dipping them into a liquid metal [1, 10]. The tubes protruded from a nanotube fiber, which was recuperated from nanotube arc deposits [11]. The tubes were not processed in any way in order to avoid contamination or damage. The conductance of the nanotubes was measured as a function of the depth L into the liquid metal. The resistance of these tubes was found to demonstrate flat quantized conductance plateaus (i.e. sample-length-independent resistance) and the tubes could ∗Permanent address: CNRS-LEPES, BP 166, 38042 Grenoble Cedex 9, France ∗∗Corresponding author. (Fax: +1-404/894-7879, E-mail: [email protected]) sustain very large currents [1]. The independence of the conductance values on the tube diameter (which were close to G0; values near 1/2G0 were also observed), the flatness of the plateaus and the very large currents (up to 1 mA through a tube) led Frank et al. to conclude that the transport was confined to the outer layer of the tube and that the transport was ballistic [1]. It appeared that the conductance of the outer layer was G0 rather than 2G0, as expected on theoretical grounds [9, 12]. At the time of publication, it was known that nanotubes were conductors (from numerous experiments), however ballistic transport had not been observed under any conditions. Subsequent experiments confirmed that only the surface of MWNTs transport the current and that very high current densities can be applied [2, 13]. Aharonov Bohm experiments [13] showed that at most only the outer two layers conduct. Furthermore, high currents will destroy the outer layers only. Since only one in three layers is expected to be metallic, it is expected statistically that only a few layers at the top can participate in the transport. Our present experiments strongly suggest that only the outer layer participates, with only the expected conductance value. However, the key result, that the transport is ballistic was contradicted in at least two experiments [2, 3]. In the experiments by Schonenberger et al. [2], it was found that the resistance per unit length of MWNTs is of the order of 5 kΩ/μm while the experiments of Bachtold et al. show even higher values (of the order of 10 kΩ/μm) [3]. Very recently, Tinkham’s group conclusively demonstrated that SWNTs are ballistic conductors by showing the quantum interference effect in the current between two electrodes [13]. The fact that SWNTs are ballistic and MWNTs are not is counter to general arguments which all tend to favor the MWNTs to have longer mean free paths [2, 15]. Here, we focus on direct measurements of , the resistance per unit length of MWNTs which can be converted to the momentum mean free paths. We concentrate on the shape of the conductance steps. It is important to realize that the mean free path is the critical parameter that determines the ballistic aspects of the conductance [16] and not the total resistance of the system, which also includes spurious contact resistances, as