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Imaging standing waves in a two-dimensional electron gas


ELECTRONS occupying surface states on the close-packed surfaces of noble metals form a two-dimensional nearly free electron gas1–3. These states can be probed using the scanning tunnelling microscope (STM), providing a unique opportunity to study the local properties of electrons in low-dimensional systems4. Here we report the direct observation of standing-wave patterns in the local density of states of the Cu(lll) surface using the STM at low temperature. These spatial oscillations are quantum-mechanical interference patterns caused by scattering of the two-dimensional electron gas off step edges and point defects. Analysis of the spatial oscillations gives an independent measure of the surface state dispersion, as well as insight into the interaction between surface-state electrons and scattering sites on the surface.

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  1. 1

    Gartland, P. O. & Slagsvold, B. J. Phys. Rev. B12, 4047–4058 (1975).

  2. 2

    Heimann, P., Neddermeyer, H. & Roloff, H. F. J. Phys. C10, L17–L22 (1977).

  3. 3

    Zangwill, A. Physics at Surfaces, Ch. 4 (Cambridge Univ. Press, Cambridge, 1988).

  4. 4

    Davis, L.C., Everson, M.P., Jaklevic, R.C. & Shen, W. Phys. Rev. B43, 3821–3880 (1991).

  5. 5

    Eigler, D.M. & Schweizer, E.K. Nature 344, 524–526 (1990).

  6. 6

    Tersoff, J. & Hamann, D.R. Phys. Rev. B31, 805–813 (1985).

  7. 7

    Lang, N.D. Phys. Rev. B 34, 5947–5950 (1986).

  8. 8

    Everson, M.P., Jaklevic, R.C. & Shen, W. J. Vac. Sci. Technol. A8, 3662–3665 (1990).

  9. 9

    Shockley, W. Phys. Rev. 56, 317–323 (1939).

  10. 10

    Forstmann, F. Z. Phys. 235, 69–74 (1970).

  11. 11

    Kevan, S.D. Phys. Rev. Lett. 50, 526–529 (1983).

  12. 12

    Ziman, J. M. Principles of the Theory of Solids, Section 5.5 (Cambridge Univ. Press, Cambridge, 1972).

  13. 13

    Brodde, A., Tosch, S.T. & Neddermeyer, H. J. Microsc. 152, 441–448 (1988).

  14. 14

    Samsavar, A. et al. Phys. Rev. Lett. 65, 1607–1610 (1990).

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