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An atlas of carbon nanotube optical transitions

Abstract

Electron–electron interactions are significantly enhanced in one-dimensional systems1, and single-walled carbon nanotubes provide a unique opportunity for studying such interactions and the related many-body effects in one dimension2,3,4. However, single-walled nanotubes can have a wide range of diameters and hundreds of different structures, each defined by its chiral index (n,m)5,6, where n and m are integers that can have values from zero up to 30 or more. Moreover, one-third of these structures are metals and two-thirds are semiconductors, and they display optical resonances at many different frequencies. Systematic studies of many-body effects in nanotubes would therefore benefit from the availability of a technique for identifying the chiral index of a nanotube based on a measurement of its optical resonances, and vice versa. Here, we report the establishment of a structure–property ‘atlas’ for nanotube optical transitions based on simultaneous electron diffraction measurements of the chiral index and Rayleigh scattering measurements of the optical resonances7,8 of 206 different single-walled nanotube structures. The nanotubes, which were suspended across open slit structures on silicon substrates, had diameters in the range 1.3–4.7 nm. We also use this atlas as a starting point for a systematic study of many-body effects in the excited states of single-walled nanotubes9,10,11,12,13,14,15,16. We find that electron–electron interactions shift the optical resonance energies by the same amount for both metallic and semiconducting nanotubes, and that this shift (which corresponds to an effective Fermi velocity renormalization) increases monotonically with nanotube diameter. This behaviour arises from two sources: an intriguing cancellation of long-range electron–electron interaction effects, and the dependence of short-range electron–electron interactions on diameter10,11.

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Figure 1: Electron diffraction patterns and Rayleigh spectra of three representative nanotubes.
Figure 2: Momentum-resolved transitions with nanotube optical resonances.
Figure 3: Renormalization of the effective Fermi velocity and its p-dependence.
Figure 4: Trigonal asymmetry.

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Acknowledgements

This study was supported by the US National Science Foundation (NSF, CAREER grant 0846648, DMR10-1006184 and EEC-0832819 to the NSF Center for Integrated Nanomechanical Systems), the US Department of Energy (DOE, DE-AC02-05CH11231 and DE-AC02-05CH11231 to the Molecular Foundry), the National Natural Science Foundation of China (91021007, 10874218, 10974238, 20973195 and 50725209) and the Chinese Ministry of Science and Technology (2009DFA01290). Computational resources were provided by the NSF (through TeraGrid resources at the National Institute for Computational Sciences) and the DOE (through the National Energy Research Scientific Computing Centre at the Lawrence Berkeley National Laboratory). R.B.C. acknowledges support from Brazilian funding agencies CNPq, FAPERJ and INCT – Nanomateriais de Carbono.

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F.W., E.W. and K.L. conceived the experiment. K.L., F.X., X.H. and F.W. carried out the optical measurements. K.L., S.A. and X.B. carried out structural characterization. K.L., W.W. and A.Z. contributed to growing the sample. J.D., R.B.C., S.G.L. and F.W. performed theoretical analysis. All authors discussed the results and wrote the paper.

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Correspondence to Enge Wang or Feng Wang.

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The authors declare no competing financial interests.

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Liu, K., Deslippe, J., Xiao, F. et al. An atlas of carbon nanotube optical transitions. Nature Nanotech 7, 325–329 (2012). https://doi.org/10.1038/nnano.2012.52

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