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Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures


The electronic transport properties of conventional three-dimensional metals are successfully described by Fermi-liquid theory. But when the dimensionality of such a system is reduced to one, the Fermi-liquid state becomes unstable to Coulomb interactions, and the conduction electrons should instead behave according to Tomonaga–Luttinger-liquid (TLL) theory. Such a state reveals itself through interaction-dependent anomalous exponents in the correlation functions, density of states and momentum distribution of the electrons1,2,3. Metallic single-walled carbon nanotubes (SWNTs) are considered to be ideal one-dimensional systems for realizing TLL states4,5,6. Indeed, the results of transport measurements on metal–SWNT and SWNT–SWNT junctions have been attributed7,8,9 to the effects of tunnelling into or between TLLs, although there remains some ambiguity in these interpretations10. Direct observations of the electronic states in SWNTs are therefore needed to resolve these uncertainties. Here we report angle-integrated photoemission measurements of SWNTs. Our results reveal an oscillation in the π-electron density of states owing to one-dimensional van Hove singularities, confirming the one-dimensional nature of the valence band. The spectral function and intensities at the Fermi level both exhibit power-law behaviour (with almost identical exponents) in good agreement with theoretical predictions for the TLL state in SWNTs.

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Figure 1: TEM images of SWNTs.
Figure 2: Photoemission spectra of SWNTs and graphite near EF measured at = 65 eV.
Figure 3: Comparison between the experimental and calculated spectra of the SWNT-A1 and SWNT-B samples.
Figure 4: High-resolution photoemission spectra of the SWNT-A2 sample near EF measured at T = 10 K, 40 K, 70 K, 150 K and 310 K with an energy resolution of 13 meV.
Figure 5: Temperature dependence of the ratio of the photoemission intensity at EF to the intensity of the S1 peak, plotted on a log–log scale.


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We thank Y. Misaki for support with TEM observations. This study was performed with the approval of the Photon Factory Advisory Committee and under the Cooperative Research Program of HiSOR, Hiroshima Synchrotron Radiation Center, Hiroshima University. This study was supported in part by a Grant-in-Aid for Science Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Correspondence to Hiromichi Kataura.

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Ishii, H., Kataura, H., Shiozawa, H. et al. Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures. Nature 426, 540–544 (2003).

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