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Quantum-well states in copper thin films

Nature volume 398, pages 132–134 (1999)Cite this article

Abstract

A standard exercise in elementary quantum mechanics is to describe the properties of an electron confined in a potential well. The solutions of Schrödinger's equation are electron standing waves—or ‘quantum-well’ states—characterized by the quantum number n, the number of half-wavelengths that span the well. Quantum-well states can be experimentally realized in a thin film, which confines the motion of the electrons in the direction normal to the film: for layered semiconductor quantum wells, the aforementioned quantization condition provides (with the inclusion of boundary phases) a good description of the quantum-well states. The presence of such states in layered metallic nanostructures isbelieved to underlie many intriguing phenomena, such as the oscillatory magnetic coupling of two ferromagnetic layers across anon-magnetic layer1,2 and giant magnetoresistance3. But our understanding of the properties of the quantum-well states in metallic structures is still limited. Here we report photoemission experiments that reveal the spatial variation of the quantum-well wavefunction within a thin copper film. Our results confirm an earlier proposal4 that the amplitude of electron waves confined in a metallic thin film is modulated by an envelope function (of longer wavelength), which plays a key role in determining the energetics of the quantum-well states.

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Figure 1: Schematic drawing of the QW wavefunctions at a given energy for ν= 1, 2 and 3.
Figure 2: Spatial variation of the QW wavefunctions mapped by photoemission.
Figure 3: Images of the photoemission energy spectra versus the total Cu thickness for the symmetrical double QW Cu/Ni/Cu.

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Acknowledgements

This work was supported by the US DOE, the US National Science Foundation, and the University of California for the conduct of discretionary research by Los Alamos National Laboratory. Z.D.Z. acknowledges the support of the National Science Foundation of China. E.A. acknowledges the support of the Miller Institute at the University of California, Berkeley.

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Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, 94720, California, USA

    R. K. Kawakami, Hyuk J. Choi, Ernesto J. Escorcia-Aparicio, M. O. Bowen, J. H. Wolfe, E. Arenholz, Z. D. Zhang & Z. Q. Qiu

  2. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA

    E. Rotenberg & N. V. Smith

  3. International Center for Materials Physics, Institute of Metal Research, Academia Sinica, 110015, Shenyang, People's Republic of China

    Z. D. Zhang

Authors
  1. R. K. Kawakami
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  2. E. Rotenberg
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  3. Hyuk J. Choi
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  4. Ernesto J. Escorcia-Aparicio
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  5. M. O. Bowen
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  6. J. H. Wolfe
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  7. E. Arenholz
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  8. Z. D. Zhang
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  9. N. V. Smith
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  10. Z. Q. Qiu
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Corresponding author

Correspondence to Z. Q. Qiu.

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Kawakami, R., Rotenberg, E., Choi, H. et al. Quantum-well states in copper thin films. Nature 398, 132–134 (1999). https://doi.org/10.1038/18178

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