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Quantum mirages formed by coherent projection of electronic structure


Image projection relies on classical wave mechanics and the use of natural or engineered structures such as lenses or resonant cavities. Well-known examples include the bending of light to create mirages in the atmosphere, and the focusing of sound by whispering galleries. However, the observation of analogous phenomena in condensed matter systems is a more recent development1, facilitated by advances in nanofabrication. Here we report the projection of the electronic structure surrounding a magnetic Co atom to a remote location on the surface of a Cu crystal; electron partial waves scattered from the real Co atom are coherently refocused to form a spectral image or ‘quantum mirage’. The focusing device is an elliptical quantum corral2,3, assembled on the Cu surface. The corral acts as a quantum mechanical resonator, while the two-dimensional Cu surface-state electrons form the projection medium. When placed on the surface, Co atoms display a distinctive spectroscopic signature, known as the many-particle Kondo resonance4,5,6, which arises from their magnetic moment. By positioning a Co atom at one focus of the ellipse, we detect a strong Kondo signature not only at the atom, but also at the empty focus. This behaviour contrasts with the usual spatially-decreasing response of an electron gas to a localized perturbation7.

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Figure 1: Detection of the Kondo resonance localized around a single Co atom on Cu(111).
Figure 2: Elliptical electron resonators.
Figure 3: Visualization of the quantum mirage.
Figure 4: Tunnelling spectra.


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We thank B. A. Jones, E. J. Heller, J. S. Hersch, G. Fiete, A. J. Heinrich and C. T. Rettner for helpful discussions, and L. Folks for expert assistance with image preparation.

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Correspondence to H. C. Manoharan.

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Manoharan, H., Lutz, C. & Eigler, D. Quantum mirages formed by coherent projection of electronic structure . Nature 403, 512–515 (2000).

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