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.

Coupling of spin and orbital motion of electrons in carbon nanotubes

Nature volume 452, pages 448–452 (2008)Cite this article

Abstract

Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion, leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes are widely believed to be four-fold degenerate1,2,3,4,5,6,7,8,9,10, owing to independent spin and orbital symmetries, and also to possess electron–hole symmetry11. Here we report measurements demonstrating that in clean nanotubes the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin–orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and antiparallel alignment for holes. Our measurements are consistent with recent theories12,13 that predict the existence of spin–orbit coupling in curved graphene and describe it as a spin-dependent topological phase in nanotubes. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of quantum bits (qubits) in nanotubes and providing a mechanism for all-electrical control of spins14 in nanotubes.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Few-electron carbon nanotube quantum dot devices.
Figure 2: Excited-state spectroscopy of a single electron in a nanotube dot.
Figure 3: The many-electron ground states and their explanation by spin-orbit interaction.
Figure 4: Theoretical model for spin–orbit interaction in nanotubes and the energy level spectroscopy of a single hole.

References

  1. Kane, C. L. & Mele, E. J. Size, shape, and low energy electronic structure of carbon nanotubes. Phys. Rev. Lett. 78, 1932–1935 (1997)

    Article  CAS  ADS  Google Scholar 

  2. Cobden, D. H. & Nygard, J. Shell filling in closed single-wall carbon nanotube quantum dots. Phys. Rev. Lett. 89, 046803 (2002)

    Article  ADS  Google Scholar 

  3. Liang, W. J., Bockrath, M. & Park, H. Shell filling and exchange coupling in metallic single-walled carbon nanotubes. Phys. Rev. Lett. 88, 126801 (2002)

    Article  ADS  Google Scholar 

  4. Jarillo-Herrero, P. et al. Electronic transport spectroscopy of carbon nanotubes in a magnetic field. Phys. Rev. Lett. 94, 156802 (2005)

    Article  CAS  ADS  Google Scholar 

  5. Jarillo-Herrero, P. et al. Orbital Kondo effect in carbon nanotubes. Nature 434, 484–488 (2005)

    Article  CAS  ADS  Google Scholar 

  6. Moriyama, S. et al. Four-electron shell structures and an interacting two-electron system in carbon-nanotube quantum dots. Phys. Rev. Lett. 94, 186806 (2005)

    Article  CAS  ADS  Google Scholar 

  7. Sapmaz, S. et al. Electronic excitation spectrum of metallic carbon nanotubes. Phys. Rev. B 71, 153402 (2005)

    Article  ADS  Google Scholar 

  8. Cao, J., Wang, Q. & Dai, H. Electron transport in very clean, as-grown suspended carbon nanotubes. Nature Mater. 4, 745–749 (2005)

    Article  CAS  ADS  Google Scholar 

  9. Makarovski, A., An, L., Liu, J. & Finkelstein, G. Persistent orbital degeneracy in carbon nanotubes. Phys. Rev. B 74, 155431 (2006)

    Article  ADS  Google Scholar 

  10. Makarovski, A., Zhukov, A., Liu, J. & Finkelstein, G. SU(2) and SU(4) Kondo effects in carbon nanotube quantum dots. Phys. Rev. B 75, 241407 (2007)

    Article  ADS  Google Scholar 

  11. Jarillo-Herrero, P. et al. Electron–hole symmetry in a semiconducting carbon nanotube quantum dot. Nature 429, 389–392 (2004)

    Article  CAS  ADS  Google Scholar 

  12. Ando, T. Spin–orbit interaction in carbon nanotubes. J. Phys. Soc. Jpn. 69, 1757–1763 (2000)

    Article  CAS  ADS  Google Scholar 

  13. Huertas-Hernando, D., Guinea, F. & Brataas, A. Spin–orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B 74, 155426 (2006)

    Article  ADS  Google Scholar 

  14. Nowack, K. C., Koppens, F. H. L., Nazarov, V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007)

    Article  CAS  ADS  Google Scholar 

  15. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A. 57, 120–126 (1998)

    Article  CAS  ADS  Google Scholar 

  16. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004)

    Article  CAS  ADS  Google Scholar 

  17. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  CAS  ADS  Google Scholar 

  18. Bulaev, D. V., Trauzettel, B. & Loss, D. Spin–orbit interaction and anomalous spin relaxation in carbon nanotube quantum dots. Preprint at 〈http://arXiv.org/abs/0712.3767〉 (2007)

  19. Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphene quantum dots. Nature Phys. 3, 192–196 (2007)

    Article  CAS  ADS  Google Scholar 

  20. Awschalom, D. D. & Flatte, M. E. Challenges for semiconductor spintronics. Nature Phys. 3, 153–159 (2007)

    Article  CAS  ADS  Google Scholar 

  21. Sahoo, S. et al. Electric field control of spin transport. Nature Phys. 1, 99–102 (2005)

    Article  CAS  ADS  Google Scholar 

  22. Tombros, N., van der Molen, S. J. & van Wees, B. J. Separating spin and charge transport in single-wall carbon nanotubes. Phys. Rev. B 73, 233403 (2006)

    Article  ADS  Google Scholar 

  23. Tombros, N. et al. Electronic spin transport and spin precession in single graphene layers at room temperature. Nature 448, 571–574 (2007)

    Article  CAS  ADS  Google Scholar 

  24. Minot, E. D., Yaish, Y., Sazonova, V. & McEuen, P. L. Determination of electron orbital magnetic moments in carbon nanotubes. Nature 428, 536–539 (2004)

    Article  CAS  ADS  Google Scholar 

  25. Cobden, D. H. et al. Spin splitting and even–odd effects in carbon nanotubes. Phys. Rev. Lett. 81, 681–684 (1998)

    Article  CAS  ADS  Google Scholar 

  26. Oreg, Y., Byczuk, K. & Halperin, B. I. Spin configurations of a carbon nanotube in a nonuniform external potential. Phys. Rev. Lett. 85, 365–368 (2000)

    Article  CAS  ADS  Google Scholar 

  27. Ralchenko et al. Atomic Spectra Database Version 3.1.3 (National Institute of Standards and Technology, Gaithersburg, Maryland) 〈http://physics.nist.gov/asd3〉 (accessed, 14 November 2007)

    Google Scholar 

Download references

Acknowledgements

We thank E. Altman, Y. Gefen, C. L. Henley, Y. Meir, E. Mueller, Y. Oreg, E. I. Rashba, A. Stern and B. Trauzettel for discussions. This work was supported by the NSF through the Center for Nanoscale systems, and by the MARCO Focused Research Center on Materials, Structures and Devices. Samples were fabricated at the Cornell node of the National Nanofabrication Users Network, funded by NSF.

Author Contributions F.K. and S.I. fabricated the devices and performed the experiments. F.K., S.I., D.C.R. and P.L.M. analysed the data and co-wrote the paper. All authors discussed the results and commented on the manuscript.

Author information

Author notes

  1. F. Kuemmeth and S. Ilani: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA,

    F. Kuemmeth, S. Ilani, D. C. Ralph & P. L. McEuen

Authors
  1. F. Kuemmeth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Ilani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. C. Ralph
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. L. McEuen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. L. McEuen.

Supplementary information

Supplementary Information

The file contains Supplementary Discussion and Supplementary Figures S1-S2 with Legends. This document discusses how the one-electron and one-hole quantum dots are identified, and how the few-electron addition spectra are affected by higher longitudinal modes. Two Figures further compare quantum dots localized over different gate electrodes and schematically contrast the effects of spin-orbit coupling and KK’ scattering. (PDF 299 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kuemmeth, F., Ilani, S., Ralph, D. et al. Coupling of spin and orbital motion of electrons in carbon nanotubes. Nature 452, 448–452 (2008). https://doi.org/10.1038/nature06822

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06822

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced 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