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Effective mass effect in attosecond electron transport

November 31, 2017

Clocking the dynamics of effective mass

The electronic band structure governs the electron dynamics in solids. It defines a group velocity and an effective mass of the electronic wave packet. Recent experimental and theoretical studies suggest that an electron acquires the effective mass of its excited state over distances much larger than the lattice period of the solid. Therefore, electron propagation on atomic length scales was typically considered to be free-electron-like. Here, we test this hypothesis by probing attosecond photoemission from a Cu(111) surface. We use attosecond pulse trains in the extreme-ultraviolet (21–33 eV) to excite electrons from two initial bands within the 3d-valence band of copper. We timed their arrival at the crystal surface with a probing femtosecond infrared pulse, and found an upper limit of 350 ± 40 as ( 1  as = 1018  s ) for the propagation time an electron requires to assume the effective mass of its excited state. This observation implies that a final-state Bloch wave packet forms within a travel distance of 5–7 Å, which is at most two atomic layers. Using well-established theory, our measurements demonstrate the importance of the band structure even for atomic-scale electron transport.


Figure 1: Fig. 1. (a) Experimental setup. The p-polarized XUV and IR beams are focused first into an argon gas target to obtain a reference RABBITT measurement. Subsequently, the pulses are refocused by a gold-coated toroidal mirror onto the copper sample at an incidence angle of 75°, and the photoelectrons are detected by a hemispherical analyzer 30° from the surface normal. A second RABBITT from copper is recorded. (b), (c), Sketch of the three-step model of photoemission. (1) Upon excitation by light, an electron is promoted from an occupied band in the valence band below the Fermi level into an unoccupied band. (2) The excited electron propagates in real space towards the solid surface. (3) The electron passes the surface barrier potential and escapes the solid, where it will then interact with the IR. With the given XUV photon energies, the typical photoelectron escape depths λ range between 5 and 7 Å.

Reference:  Kasmi, L., M. Lucchini, L. Castiglioni, P. Kliuiev, J. Osterwalder, M. Hengsberger, L. Gallmann, P. Krüger and U. Keller (2017). Effective mass effect in attosecond electron transport. Optica 4: 1492-1497. (10.1364/OPTICA.4.001492) Kasmi-2017 (1.34 MB).

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