Luttinger Liquid Behavior in Carbon Nanotubes

An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a Luttinger liquid (LL

Luttinger Liquid Behavior in Carbon Nanotubes

Marc Bockrath*, David H. Cobden*, Jia Lu*, Andrew G. Rinzler+, Richard E. Smalley+, Leon Balents#

and Paul L. McEuen*

*Department of Physics, University of California and Materials Sciences Division, Lawrence Berkeley NationalLaboratory, Berkeley, California, 94720

+Center for Nanoscale Science and Technology, Rice Quantum Institute, and Department of Chemistry and Physics,MS-100, Rice University, P.O. Box 1892, Houston, TX 77251

#Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030

An interacting one-dimensional (1D) electron system is predicted to behave very differently thanits higher-dimensional counterparts.1 Coulomb interactions strongly modify the properties awayfrom those of a Fermi liquid, resulting in a Luttinger liquid (LL) characterized by a power-lawvanishing of the density of states at the Fermi level. Experiments on one-dimensionalsemiconductor wires2 and fractional quantum Hall conductors3,4,5,6 have been interpreted using thispicture, but questions remain about the connection between theory and experiment. Recently,single-walled carbon nanotubes (SWNTs) have emerged as a new type of 1D conductor7,8,9,10 thatmay exhibit LL behavior11,12. Here we present measurements of the conductance of individualropes of such SWNTs as a function of temperature and voltage. Power law behavior as a functionof temperature or bias voltage is observed: G~ Tα and dI/dV ~ Vα. Both the power-law functionalforms and the inferred exponents are in good agreement with theoretical predictions for tunnelinginto a LL.

Since the initial discovery of SWNTs, experiments have revealed a great deal about their electronicproperties. STM measurements of individual tubes have verified that they are either 1D semiconductorsor conductors, depending upon their chirality7,8. Electrodes have also been attached to nanotubes andropes of nanotubes to probe transport. These electrodes make tunneling contacts to the tubes and, for

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