Effective mass effect in attosecond electron transport

The energy-dependence or dispersion of the electronic band structure influences the electron dynamics and defines a group velocity and an effective mass of the electronic wave packet. Theory assumes that an electron acquires its effective mass over distances much larger than the lattice period of the solid. Therefore, electron propagation on atomic length scales was typically considered as free-electron-like. Here we report an upper limit of 320 ± 40 as (1 as = 10¯¹⁸ seconds) 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. We used attosecond pulse trains in the extreme-ultraviolet (21-33 eV) to excite electrons from two initial bands within the 3d-valence band of copper and timed their arrival at the crystal surface with a probing femtosecond infrared pulse. Using well established theory, our measurements demonstrate the role of the band structure in atomic scale electron transport.