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Snell's law for surface electrons: Refraction of an electron gas imaged in real space

Project overview

On the close-packed surfaces of noble metals exists a surface state. The electrons in the surface state form a two-dimensional electron gas. Scattering of the electrons in the surface state forms the well-known standing wave patterns. It is known that these surface states survive as interface states below ordered adsorbate layers. In the case of Xe/Cu(111) these interface states were imaged recently with a scanning tunneling microscope at low temperatures.

We have grown ultrathin sodium chloride layers (two monolayers) on a copper (111) surface and have observed the existence of an interface state located at the NaCl/Cu interface, descending from the original Cu(111) surface state. Several images of the same region near a NaCl step edge, taken at various voltages, show that the wavelength of the NaCl/Cu(111) interface state is larger than that of the Cu(111) surface state (see images a-d). Detailed spectroscopic experiments at 8 K determined the bottom of the interface band to be about 225 meV below the Fermi level. A small increase of the effective mass of the electrons is observed. The phase-accumulation model provides a qualitative understanding of the observed changes in the dispersion. Even more relevant, it reveals that the wave functions of the surface electrons are barely modified upon adsorption of NaCl, which makes a high transmission through NaCl step edges promising.

The misalignment between the NaCl lattice and the underlying Cu surface forms a Moiré pattern observed in atomically resolved STM images. This additional periodicity produces a splitting in the band structure of the interface state of about 50 meV at 20-400 meV above the Fermi level, depending on the specific rotation of the NaCl domain. The electron density just above and just below the band gap is strongly modulated as can be seen in corresponding STM images. The strong standing plane waves just below the band gap allows us to study the refraction of two-dimensional electron waves at the NaCl island edges as shown. The Moiré-pattern-induced band gap shows a new way to tailor the properties of a two-dimensional electron gas for future applications. These possibilities can be further extended by controlled sequential growth of different dielectric materials. In contrast to surface states, interface states are inherently protected by the dielectric adlayer and can even be studied under ambient conditions.

 References

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A. Hotzel, G. Moos, K. Ishioka, M. Wolf, G. Ertl, Appl. Phys. B 68, 615 (1999).

J.-Y. Park, U. D. Ham, S.-J. Kahng, Y. Kuk, K. Miyake, K. Hata, and H. Shigekawa, Phys. Rev. B 62, R16341 (2000).

N. V. Smith, Phys. Rev. B 32, 3549 (1985).

J. Repp, G. Meyer, K. H. Rieder, Phys. Rev. Lett., 92(3) 036803 (2004).

Images, click to enlarge
Dispersion.
Dispersion
Electron refraction.
Electron refraction
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