Electron-hole symmetry in a semiconducting carbon nanotube quantum dot

Abstract

Optical and electronic phenomena in solids arise from the behaviour of electrons and holes (unoccupied states in a filled electron sea). Electron–hole symmetry can often be invoked as a simplifying description, which states that electrons with energy above the Fermi sea behave the same as holes below the Fermi energy. In semiconductors, however, electron–hole symmetry is generally absent, because the energy-band structure of the conduction band differs from the valence band1. Here we report on measurements of the discrete, quantized-energy spectrum of electrons and holes in a semiconducting carbon nanotube2. By applying a voltage to a gate electrode, an individual nanotube is filled controllably with a precise number of either electrons or holes, starting from one. The discrete excitation spectrum for a nanotube with N holes is strikingly similar to the corresponding spectrum for N electrons. This observation of near-perfect electron–hole symmetry3 demonstrates that a semiconducting nanotube can be free of charged impurities, even in the limit of few electrons or holes. We furthermore find an anomalously small Zeeman spin splitting and an excitation spectrum indicating strong electron–electron interactions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Sample and characterization.
Figure 2: Few-hole semiconducting nanotube.
Figure 3: Excitation spectra for different electron and hole numbers demonstrating electron–hole symmetry. dI/dV is plotted versus (V, VG) at T = 0.3 K.
Figure 4: Electron–hole symmetry in semiconducting SWNTs.

References

  1. 1

    Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College, Orlando, 1976)

    Google Scholar 

  2. 2

    Dekker, C. Carbon nanotubes as molecular quantum wires. Phys. Today 52, 22–28 (1999)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Dresselhaus, M. S., Dresselhaus, G. & Eklund, P. C. Science of Fullerenes and Carbon Nanotubes (Academic, San Diego, 1996)

    Google Scholar 

  4. 4

    Kouwenhoven, L. P., Austing, D. G. & Tarucha, S. Few-electron quantum dots. Rep. Prog. Phys. 64, 701–736 (2001)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Tans, S. J. et al. Individual single-wall nanotubes as quantum wires. Nature 386, 474–477 (1997)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Bockrath, M. et al. Single-electron transport in ropes of carbon nanotubes. Science 275, 1922–1925 (1997)

    CAS  Article  Google Scholar 

  7. 7

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

    ADS  Article  Google Scholar 

  8. 8

    Ando, T. & Nakanishi, T. Impurity scattering in carbon nanotubes—Absence of back scattering. Jpn. J. Appl. Phys. 67, 1704–1713 (1998)

    CAS  Article  Google Scholar 

  9. 9

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

    ADS  CAS  Article  Google Scholar 

  10. 10

    Bronikowski, M. J., Willis, P. A., Colbert, D. T., Smith, K. A. & Smalley, R. E. Gas-phase production of carbon single-walled nanotubes from carbon monoxide via the HiPco process: A parametric study. J. Vacuum Sci. Technol. A 19, 1800–1805 (2001)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Fuhrer, M. S. et al. Crossed nanotube junctions. Science 288, 494–497 (2000)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Nygård, J. & Cobden, D. H. Quantum dots in suspended single-wall carbon nanotubes. Appl. Phys. Lett. 79, 4216–4218 (2001)

    ADS  Article  Google Scholar 

  13. 13

    Bachtold, A., Hadley, P., Nakanishi, T. & Dekker, C. Logic circuits with carbon nanotube transistors. Science 294, 1317–1320 (2001)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Park, J. & McEuen, P. L. Formation of a p-type quantum dot at the end of an n-type carbon nanotube. Appl. Phys. Lett. 79, 1363–1365 (2001)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Postma, H. W. C., Sellmeijer, A. & Dekker, C. Manipulation and imaging of individual single-wall carbon nanotubes with an atomic force microscope. Adv. Mater. 12, 1299–1302 (2000)

    CAS  Article  Google Scholar 

  16. 16

    Postma, H. W. C., Yao, Z. & Dekker, C. Electron addition and excitation spectra of individual single-wall carbon nanotubes. J. Low-Temp. Phys. 118, 495–507 (2000)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Heinze, S. et al. Carbon nanotubes as Schottky barrier transistors. Phys. Rev. Lett. 89, 106801 (2002)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Grabert, H. & Devoret, M. H. Single Charge Tunneling (Plenum, New York, 1992)

    Google Scholar 

  19. 19

    Park, H. et al. Nano-mechanical oscillations in a single-C60 transistor. Nature 407, 57–60 (2000)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Häusler, W. & Kramer, B. Interacting electrons in a one-dimensional quantum dot. Phys. Rev. B 47, 16353–16357 (1993)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank R. E. Smalley and co-workers for providing the high-quality HiPco nanotubes, and S. De Franceschi, J. Kong, K. Williams, Y. Nazarov, H. Postma, S. Lemay and J. Fernández-Rossier for discussions. We acknowledge the technical assistance of R. Schouten, B. van der Enden and M. van Oossanen. Financial support was obtained from the Dutch Organization for Fundamental Research (FOM).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Pablo Jarillo-Herrero.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Supplementary Figures

FigS1 shows a scheme of the band diagram. FigS2 shows additional data from a different semiconducting nanotube. FigS3 shows Zeeman splitting in a magnetic field. (PDF 1585 kb)

Supplementary Discussion

Supplementary discussion/legends related to the supplementary figures; 1) Model calculations; 2) Scattering and disorder; 3) Zeeman splitting. (DOC 29 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jarillo-Herrero, P., Sapmaz, S., Dekker, C. et al. Electron-hole symmetry in a semiconducting carbon nanotube quantum dot. Nature 429, 389–392 (2004). https://doi.org/10.1038/nature02568

Download citation

Further reading

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.