The propagation and transport of electrons in crystals is a fundamental process pertaining to the functioning of most electronic devices. Microscopic theories describe this phenomenon as being based on the motion of Bloch wave packets1. These wave packets are superpositions of individual Bloch states with the group velocity determined by the dispersion of the electronic band structure near the central wavevector in momentum space1. This concept has been verified experimentally in artificial superlattices by the observation of Bloch oscillations2—periodic oscillations of electrons in real and momentum space. Here we present a direct observation of electron wave packet motion in a real-space and real-time experiment, on length and time scales shorter than the Bloch oscillation amplitude and period. We show that attosecond metrology3 (1 as = 10−18 seconds) now enables quantitative insight into weakly disturbed electron wave packet propagation on the atomic length scale without being hampered by scattering effects, which inevitably occur over macroscopic propagation length scales. We use sub-femtosecond (less than 10−15 seconds) extreme-ultraviolet light pulses3 to launch photoelectron wave packets inside a tungsten crystal that is covered by magnesium films of varied, well-defined thicknesses of a few ångströms4. Probing the moment of arrival of the wave packets at the surface with attosecond precision reveals free-electron-like, ballistic propagation behaviour inside the magnesium adlayer—constituting the semi-classical limit of Bloch wave packet motion. Real-time access to electron transport through atomic layers and interfaces promises unprecedented insight into phenomena that may enable the scaling of electronic and photonic circuits to atomic dimensions. In addition, this experiment allows us to determine the penetration depth of electrical fields at optical frequencies at solid interfaces on the atomic scale.
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This research was supported by the Munich-Centre for Advanced Photonics. C.L., G.W. and J.B. acknowledge support by the FWF special research programs SFB-041 (ViCoM) and SFB-049 (NextLite) and project P21141-N16. G.W. is supported by the International Max Planck Research School for Advanced Photon Science (IMPRS-APS). R.K. acknowledges an ERC Starting Grant. Calculations have been performed on the Vienna Scientific Cluster. S.N. and P.F. thank the Helmholtz Zentrum Berlin for support. We thank P. Echenique, E. E. Krasovskii, A. Kazansky and A. D. Sanchez-Portal for discussions.
The authors declare no competing financial interests.
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Neppl, S., Ernstorfer, R., Cavalieri, A. et al. Direct observation of electron propagation and dielectric screening on the atomic length scale. Nature 517, 342–346 (2015). https://doi.org/10.1038/nature14094
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