One-dimensional transport in bundles of single-walled carbon nanotubes

We report measurements of the temperature and gate voltage dependence for individual bundles (ropes) of single-walled nanotubes. When the conductance is less than about e/h at room temperature, it is found to decrease as an approximate power law of temperature down to the region where Coulomb blockade sets in. The power-law exponents are consistent with those expected for electron tunneling into a Luttinger liquid. When the conductance is greater than e/h at room temperature, it changes much more slowly at high temperatures, but eventually develops very large fluctuations as a function of gate voltage when sufficiently cold. We discuss the interpretation of these results in terms of transport through a Luttinger liquid. The strength and extended length of single-walled carbon nanotubes makes it quite straightforward to attach metallic electrodes to them. This has enabled several recent studies of the transport properties of individual tubes and ropes (ordered bundles of tubes) [1–5]. In most of these studies the conductance at low temperature T is found to be dominated by Coulomb blockade (CB). Here we also include measurements on ropes with high conductance and weak T dependences which do not show CB [10]. We analyse the characteristics of all our devices in the light of predictions that electrons in nanotubes should form Luttinger liquids. Each device consists of an individual nanotube rope [6], containing between 1 and ∼ 20 tubes lying on a thermally grown SiO2 surface and contacted with gold electrodes patterned by electron beam lithography. The electrode separation is 0.2 or 0.5 μm, and the metallically doped silicon substrate beneath the 0.3or 1.0-μm thick SiO2 is used as a gate electrode. We have two varieties of devices: ‘end-contacted’, where the electrode metal is deposited on top of the rope; and ‘bulk-contacted’, where the rope is deposited on top of prefabricated electrodes. An atomic force microscope (AFM) image of a typical device is inset to Fig. 1. In all the measurements reported here, the two-terminal dc current-voltage (I-V ) -1 0 1 2 0.0 0.1 0.2 0.3 0.4 0.5 T (K)