Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes

Abstract

Surface plasmons1, collective oscillations of conduction electrons, hold great promise for the nanoscale integration of photonics and electronics1,2,3,4. However, nanophotonic circuits based on plasmons have been significantly hampered by the difficulty in achieving broadband plasmonic waveguides that simultaneously exhibit strong spatial confinement, a high quality factor and low dispersion. Quantum plasmons, where the quantum mechanical effects of electrons play a dominant role, such as plasmons in very small metal nanoparticles5,6 and plasmons affected by tunnelling effects7, can lead to novel plasmonic phenomena in nanostructures. Here, we show that a Luttinger liquid8,9 of one-dimensional Dirac electrons in carbon nanotubes10,11,12,13 exhibits quantum plasmons that behave qualitatively differently from classical plasmon excitations. The Luttinger-liquid plasmons propagate at ‘quantized’ velocities that are independent of carrier concentration or excitation wavelength, and simultaneously exhibit extraordinary spatial confinement and high quality factor. Such Luttinger-liquid plasmons could enable novel low-loss plasmonic circuits for the subwavelength manipulation of light.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Infrared s-SNOM of one-dimensional plasmons in carbon nanotubes.
Figure 2: Luttinger-liquid plasmons in carbon nanotubes.
Figure 3: Quantized Luttinger-liquid plasmon propagation velocity.
Figure 4: Long-range quantum plasmons in nanotubes.

References

  1. Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).

    Article  ADS  Google Scholar 

  2. Gramotnev, D. K. & Bozhevolnyi, S. I. Plasmonics beyond the diffraction limit. Nature Photon. 4, 83–91 (2010).

    Article  ADS  Google Scholar 

  3. Schuller, J. A. et al. Plasmonics for extreme light concentration and manipulation. Nature Mater. 9, 193–204 (2010).

    Article  ADS  Google Scholar 

  4. Pendry, J. B., Aubry, A., Smith, D. R. & Maier, S. A. Transformation optics and subwavelength control of light. Science 337, 549–552 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  5. Halperin, W. P. Quantum size effects in metal particles. Rev. Mod. Phys. 58, 533–606 (1986).

    Article  ADS  Google Scholar 

  6. Scholl, J. A., Koh, A. L. & Dionne, J. A. Quantum plasmon resonances of individual metallic nanoparticles. Nature 483, 421–427 (2012).

    Article  ADS  Google Scholar 

  7. Tan, S. F. et al. Quantum plasmon resonances controlled by molecular tunnel junctions. Science 343, 1496–1499 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  8. Luttinger, J. M. An exactly soluble model of a many-fermion system. J. Math. Phys. 4, 1154–1162 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  9. Voit, J. One-dimensional Fermi liquids. Rep. Prog. Phys. 58, 977–1116 (1995).

    Article  ADS  Google Scholar 

  10. Kane, C., Balents, L. & Fisher, M. P. A. Coulomb interactions and mesoscopic effects in carbon nanotubes. Phys. Rev. Lett. 79, 5086–5089 (1997).

    Article  ADS  Google Scholar 

  11. Egger, R. & Gogolin, A. O. Effective low-energy theory for correlated carbon nanotubes. Phys. Rev. Lett. 79, 5082–5085 (1997).

    Article  ADS  Google Scholar 

  12. Bockrath, M. et al. Luttinger-liquid behaviour in carbon nanotubes. Nature 397, 598–601 (1999).

    Article  ADS  Google Scholar 

  13. Yao, Z., Postma, H. W. C., Balents, L. & Dekker, C. Carbon nanotube intramolecular junctions. Nature 402, 273–276 (1999).

    Article  ADS  Google Scholar 

  14. Liu, K. et al. An atlas of carbon nanotube optical transitions. Nature Nanotech. 7, 325–329 (2012).

    Article  ADS  Google Scholar 

  15. Ando, T., Nakanishi, T. & Saito, R. Berry's phase and absence of back scattering in carbon nanotubes. J. Phys. Soc. Jpn 67, 2857–2862 (1998).

    Article  ADS  Google Scholar 

  16. McEuen, P. L., Bockrath, M., Cobden, D. H., Yoon, Y. G. & Louie, S. G. Disorder, pseudospins, and backscattering in carbon nanotubes. Phys. Rev. Lett. 83, 5098–5101 (1999).

    Article  ADS  Google Scholar 

  17. Javey, A., Guo, J., Wang, Q., Lundstrom, M. & Dai, H. J. Ballistic carbon nanotube field-effect transistors. Nature 424, 654–657 (2003).

    Article  ADS  Google Scholar 

  18. Park, J. Y. et al. Electron–phonon scattering in metallic single-walled carbon nanotubes. Nano Lett. 4, 517–520 (2004).

    Article  ADS  Google Scholar 

  19. Purewal, M. S. et al. Scaling of resistance and electron mean free path of single-walled carbon nanotubes. Phys. Rev. Lett. 98, 186808 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Hillenbrand, R., Knoll, B. & Keilmann, F. Pure optical contrast in scattering-type scanning near-field microscopy. J. Microsc. 202, 77–83 (2001).

    Article  MathSciNet  Google Scholar 

  22. Bechtel, H. A., Muller, E. A., Olmon, R. L., Martin, M. C. & Raschke, M. B. Ultrabroadband infrared nanospectroscopic imaging. Proc. Natl Acad. Sci. USA 111, 7191–7196 (2014).

    Article  ADS  Google Scholar 

  23. Gerber, J. A., Berweger, S., O'Callahan, B. T. & Raschke, M. B. Phase-resolved surface plasmon interferometry of graphene. Phys. Rev. Lett. 113, 055502 (2014).

    Article  ADS  Google Scholar 

  24. Boltasseva, A. & Atwater, H. A. Low-loss plasmonic metamaterials. Science 331, 290–291 (2011).

    Article  ADS  Google Scholar 

  25. Arnold, M. S., Green, A. A., Hulvat, J. F., Stupp, S. I. & Hersam, M. C. Sorting carbon nanotubes by electronic structure using density differentiation. Nature Nanotech. 1, 60–65 (2006).

    Article  ADS  Google Scholar 

  26. Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).

    Article  ADS  Google Scholar 

  27. Chen, J. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).

    Article  ADS  Google Scholar 

  28. Liu, K. H. et al. High-throughput optical imaging and spectroscopy of individual carbon nanotubes in devices. Nature Nanotech. 8, 917–922 (2013).

    Article  ADS  Google Scholar 

  29. Palik, E. D. Handbook of Optical Constants of Solids (Elsevier, 1997).

    Google Scholar 

  30. Suzuura, H. & Ando, T. Phonons and electron–phonon scattering in carbon nanotubes. Phys. Rev. B 65, 235412 (2002).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank M. Raschke for discussions. H.B. and M.M., in particular, thank M. Raschke and his group for the years of pioneering research on infrared near-field techniques and key collaborations that led to the development of a near-field infrared instrument at the Advanced Light Source (ALS). The authors also thank K. Liu, Y. Sun, S. Shi, C. Jin and H. Chang for their help with sample preparation and discussions. This work was primarily supported by the Office of Basic Energy Science, Department of Energy (contract no. DE-AC02-05CH11231, Sub-Wavelength Metamaterial Program; contract no. DE-SC0003949, Early Career Award). Spectroscopy of nanotubes in the visible range was supported by the National Science Foundation (grant no. DMR-1404865). The ALS is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy (contract no. DE-AC02-05CH11231). F.W. acknowledges support from a David and Lucile Packard fellowship.

Author information

Authors and Affiliations

Authors

Contributions

F.W. and Z.S. conceived the project. Z.S. and X.H. prepared the nanotube samples. Z.S., H.B. and M.C.M. performed the near-field infrared measurements. X.H. and Z.B. performed visible spectroscopy. K.W. and T.T. provided the hBN crystals. X.H., Z.S., Y.R.S. and F.W. analysed the data. All authors discussed the results and contributed to writing the manuscript.

Corresponding authors

Correspondence to Zhiwen Shi or Feng Wang.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 476 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shi, Z., Hong, X., Bechtel, H. et al. Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes. Nature Photon 9, 515–519 (2015). https://doi.org/10.1038/nphoton.2015.123

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2015.123

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing