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 an electronic bound state above a potential well

Abstract

SHORTLY after the birth of quantum mechanics, von Neumann and Wigner made the remarkable proposal1 that certain spatially oscillating attractive potentials could support bound states at energies above the potential barriers (that is, spatially confined states within the continuum) by means of diffractive interference. Because of their unusual geometry, such potentials were regarded as mathematical curiosities2,3, although more recently it has been suggested that they might be found in certain atomic and molecular systems4,5. Following the observation of discrete electronic states in ultra-thin semiconductor layered structures6,7 (for example, in quantum wells), Stillinger8 and Herrick9 proposed that super-lattices might be used to construct potentials supporting these 'positive energy' bound states. Here we report direct evidence of such states in semiconductor heterostructures grown by molecular-beam epitaxy10. Infrared absorption measurements reveal a narrow, isolated transition from a bound state within a quantum well to a bound state at an energy greater than the barrier height; this state is spatially localized by Bragg reflections.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Similar content being viewed by others

References

  1. von Neumann, J. & Wigner, E. Phys. Z. 30, 465–467 (1929).

    Google Scholar 

  2. Simon, B. Commun. pure appl. Math. 22, 531–538 (1969).

    Article  Google Scholar 

  3. Weidmann, J. Math. Z. 98, 268–302 (1967).

    Article  MathSciNet  Google Scholar 

  4. Stillinger, F. H. & Weber, T. A. Phys. Ref. A. 10, 1122–1130 (1974).

    Article  ADS  CAS  Google Scholar 

  5. Stillinger, F. H. & Herrick, D. R. Phys. Rev. A. 11, 446–454 (1975).

    Article  ADS  CAS  Google Scholar 

  6. Esaki, L. & Chang, L. L. Phys. Rev. Lett. 33, 495–498 (1974).

    Article  ADS  CAS  Google Scholar 

  7. Dingle, R., Wiegmann, W. & Henry, C. H. Phys. Rev. Lett. 33, 827–830 (1974).

    Article  ADS  CAS  Google Scholar 

  8. Stillinger, F. H. Physica B 85, 270–276 (1977).

    Google Scholar 

  9. Herrick, D. R. Physica B 85, 44–50 (1977).

    Google Scholar 

  10. Cho, A. Y. J. Cryst. Growth 111, 1–13 (1991).

    Article  ADS  CAS  Google Scholar 

  11. Bastard, G. Wave Mechanics Applied to Heterostructures (Editions de Physique, Paris, 1990).

    Google Scholar 

  12. Nelson, D. F., Miller, R. C. & Kleinman, D. A. Phys. Rev. B 35, 7770–7773 (1981).

    Article  Google Scholar 

  13. Macleod, H. A. Thin Film Optical Filters 2nd Edn, Ch. 7, 244 (Macmillan, New York, 1986).

    Book  Google Scholar 

  14. Beltram, F. et al. Phys. Rev. Lett. 64, 3167–3170 (1990).

    Article  ADS  CAS  Google Scholar 

  15. West, L. C. & Eglash, S. J. Appl. Phys. Lett. 46, 1156–1158 (1985).

    Article  ADS  CAS  Google Scholar 

  16. Levine, B. F. et al. Appl. Phys. Lett. 52, 1481–1483 (1988).

    Article  ADS  CAS  Google Scholar 

  17. Iga, K., Uenohara, H. & Koyama, F. Electron Lett. 22, 1008–1010 (1986).

    Article  ADS  Google Scholar 

  18. Takagi, T., Koyama, F. & Iga, K. Appl. Phys. Lett. 59, 2877–2879 (1991).

    Article  ADS  CAS  Google Scholar 

  19. Lenz, G. & Salzman, J. Appl. Phys. Lett. 56, 871–873 (1990).

    Article  ADS  CAS  Google Scholar 

  20. Brener, I. et al. Quantum Electronics and Laser Science Conf. 1992 OSA Technical Digest Series. Vol. 13, 216–217 (Optical Society of America, Washington DC, 1992).

    Google Scholar 

  21. Sirtori, C., Capasso, F., Sivco, D. L. & Cho, A. Y. Appl. Phys. Lett. 60, 2678–2680 (1992).

    Article  ADS  CAS  Google Scholar 

  22. Shen, H., Pollack, F. H. & Tsu, R. Appl. Phys. Lett. 57, 13–15 (1990).

    Article  ADS  CAS  Google Scholar 

  23. Capasso, F. Science 235, 172–176 (1987).

    Article  ADS  CAS  Google Scholar 

  24. Analogies in Optics and Microelectronics (eds van Hoeninger, W. & Lenstra, D.) (Kluwer, Dordrecht, 1990).

  25. Gaylord, T. K. & Brennan, K. F. J. appl. Phys. 65, 814–820 (1989).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Capasso, F., Sirtori, C., Faist, J. et al. Observation of an electronic bound state above a potential well. Nature 358, 565–567 (1992). https://doi.org/10.1038/358565a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/358565a0

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

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